List of poster contributions
| Alba, Vincenzo | Entanglement spreading after a geometric quench in quantum spin chains | Abstract |
| Bröcker, Peter | Entanglement entropies for many-fermion systems | Abstract |
| Davenport, Simon | Entanglement Hamiltonian for composite fermion fractional quantum Hall states | Abstract |
| Desbuquois, Rémi | Experimental realization of the Haldane model | Abstract |
| Dhochak, Kusum | Spontaneous layer polarization and conducting domain walls in bilayer graphene | Abstract |
| Ejima, Satoshi | Spectral and entanglement properties of the bosonic Haldane insulator | Abstract |
| Fuji, Yohei | Symmetry protection of disordered phases and phase transitions in spin ladders | Abstract |
| Grushin, Adolfo González | Floquet fractional Chern insulators | Abstract |
| He, Yin-Chen | DMRG study on topological spin liquid and their phase transition | Abstract |
| Hormozi, Layla | Multi-layer Fractional Quantum Hall States in Lattice Systems | Abstract |
| Huang, Ching-Yu | Classification of topologically ordered phases | Abstract |
| Koch-Janusz, Maciej | Interacting and fractional topological insulators via the Z_2 chiral anomaly | Abstract |
| Lahtinen, Ville | Constructing exactly solvable spin models with given critical points from condensate-induced transitions | Abstract |
| Li, Wei | Topology and criticality in resonating AKLT-loop spin liquid states | Abstract |
| Maksymenko, Mykola | Responses of a topological superconducting wire to the static and dynamic perturbation | Abstract |
| Morampudi, Siddhardh | Numerical study of a transition between Z_2 topologically ordered phases | Abstract |
| Motruk, Johannes | Phases of spinless fermions on the honeycomb lattice from infinite density matrix renormalization group calculations | Abstract |
| Möller, Gunnar | Exactly solvable two-body Hamiltonian for the coupled Pfaffian state of two-component bosons | Abstract |
| Nielsen, Anne Ersbak Bang | Fractional quantum Hall states in lattices and physical implementation | Abstract |
| O'Brien, Aroon | MERA for spin chains with symmetry-protected topological order | Abstract |
| Ralko, Arnaud | Supersolidity hierarchy of spin-1/2 bosons in a triangular lattice | Abstract |
| Répellin, Cécile | The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus | Abstract |
| Ringel, Zohar | Disentanglers for SPT phases | Abstract |
| Roy, Bitan | Weak coupling instabilities in strained graphene: Theory of competing magnetic, topological, and charge-density wave orders | Abstract |
| Roy, Sthitadhi | Tunnel magentoresistance scan of a pristine 3D topological insulators surfaces | Abstract |
| Roychowdhury, Krishanu | Probing topological nature of many-body ground state for a system of particles on a Kagome lattice at fractional fillings | Abstract |
| Ruhman, Jonathan | Topological states in a one-dimensional fermi gas with attractive interactions | Abstract |
| Schuch, Norbert | Topological order and symmetries in tensor network models | Abstract |
| Singh, Rajeev | Many-body localization and entanglement in disordered quantum spin models | Abstract |
| Sterdyniak, Antoine | Two leg bosonic ladder in an external magnetic field at unit filling | Abstract |
| Varjas, Dániel | Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling | Abstract |
| Entanglement spreading after a geometric quench in quantum spin chains Alba, Vincenzo (LMU Munich, Department für Physik, München, Germany) |
| We investigate the entanglement spreading in the anisotropic spin-1/2 Heisenberg (XXZ) chain after a geometric quench. This corresponds to a sudden change of the geometry of the chain or, in the equivalent language of interacting fermions confined in a box trap, to a sudden increase of the trap size. The entanglement dynamics after the quench is associated with the ballistic propagation of a magnetization wavefront. At the free fermion point (XX chain), the von-Neumann entropy S_A exhibits several intriguing dynamical regimes. Specifically, at short times a logarithmic increase is observed, similar to local quenches. This is accurately described by an analytic formula that we derive from heuristic arguments. At intermediate times partial revivals of the short-time dynamics are superposed with a power-law increase S_A t^alpha, with alpha<1. Finally, at very long times a steady state develops with constant entanglement entropy. As expected, since the model is integrable, we find that the steady state is non thermal, although it exhibits extensive entanglement entropy. We also investigate the entanglement dynamics after the quench from a finite to the infinite chain (sudden expansion). While at long times the entanglement vanishes, we demonstrate that its relaxation dynamics exhibits a number of scaling properties. Finally, we discuss the short-time entanglement dynamics in the XXZ chain in the gapless phase. The same formula that describes the time dependence for the XX chain remains valid in the whole gapless phase. |
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| Entanglement Entropies for Many-Fermion Systems Bröcker, Peter (University of Cologne, Institute for Theoretical Physics, Cologne, Germany) |
| The precise determination of the entanglement of an interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harboring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions. With the entanglement entropy emerging as one of the central measures of entanglement, recent progress has focused on a precise characterization of its scaling behavior, in particular in the determination of (subleading) corrections to the prevalent boundary-law. While much progress has been made for spin and bosonic quantum many-body systems, fermion systems have proved to be more difficult. For a large class of interacting fermionic systems, the numerical method of choice for unbiased, large-scale simulations is Determinantal Quantum Monte Carlo (DQMC) for which a generalization of the replica techniques developed to calculate entanglement entropies for spin and bosonic systems has remained an open question. Here we show one possibility how to construct the corresponding algorithm in DQMC and demonstrate its strength by studying the one-dimensional Hubbard systems. We also compare our results to another recent approach based on free fermion Green’s functions. |
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| Majorana modes and p-wave superfluids for fermionic atoms in optical lattices Büchler, Hans Peter (Universität Stuttgart, Institut für Theoretische Physik III, Stuttgart, Germany) |
| We present a simple approach to create a strong p-wave interaction for fermions in an optical lattice. The crucial step is that the combination of a lattice setup with different orbital states and s-wave interactions can give rise to a strong induced p-wave pairing. We identify different topological phases and demonstrate that the setup offers a natural way to explore the transition from Kitaev's Majorana wires to two-dimensional p-wave superfluids. We demonstrate how this design can induce Majorana modes at edge dislocations in the optical lattice, and we provide an experimentally feasible protocol for the observation of the non-Abelian statistics. |
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| Entanglement Hamiltonian for composite fermion fractional quantum Hall states Davenport, Simon (University of Cambridge, Theory of Condensed Matter (TCM), Cavendish Laboratory, Cambridge, United Kingdom) |
| We present some results on the construction of an entanglement Hamiltonian for composite fermion fractional quantum Hall states, extending the recent work of Dubail, Read and Rezayi (Phys. Rev. B 86, 245310). Comparisons are made with the real space entanglement spectrum of the ground state composite fermion wave functions calculated for large system sizes (Rodríguez et al. Phys. Rev. B 88, 155307). |
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| Experimental realization of the Haldane model Desbuquois, Rémi (ETH Zurich, Institut für Quantenelektronik, Zürich, Switzerland) |
| A topologically non-trivial band structure appears in a hexagonal lattice if time-reversal symmetry is broken, as suggested by F. D. M. Haldane. He further pointed out that, in combination with broken inversion symmetry, this gives rise to a phase diagram reminiscent of the integer Quantum Hall effect, yet without the necessity of a magnetic field. Studying the band structure of a hexagonal lattice with broken time reversal symmetry induced by complex valued next-nearest neighbor couplings, he showed that the boundaries of the topologically different phases are gap opening-and-closing transitions at the Dirac points. Whilst a realization of this model in a material was hardly conceivable, it provided the conceptual basis for other topological insulators and the quantum spin Hall effect. Prospects to realize the model with cold atoms emerged by advances in generating effective magnetic fields for neutral atoms and the idea to employ time-dependent fields to break time-reversal symmetry in a hexagonal lattice. Here we report on the implementation of the Haldane model in a periodically driven honeycomb optical lattice and the characterization of the topological Bloch bands using non-interacting fermionic atoms. Modulating the position of the lattice sites along a circular trajectory generates complex next-nearest-neighbor tunneling and a gap opens at the Dirac points, which we measure using momentum-resolved inter-band transitions. In analogy to a Hall conductance we observe a characteristic displacements of the atomic cloud under a constant force. By additionally breaking the inversion-symmetry, we identify the closing of the gap at an individual Dirac point, associated with the transition between the topologically distinct phases, obtaining good agreement with the calculated phase diagramm. Whilst the physics of the non-interacting system is determined by the single-particle band structure, as studied in this work, the cold atom systems is also suited to explore the interplay between topology and interactions. |
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| Spontaneous layer polarization and conducting domain walls in bilayer graphene Dhochak, Kusum (Weizmann Institute of Science, Condensed Matter Physics, Rehovot, Israel) |
| Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different quantum Hall ferromagnetic phases, resulting from an interplay from the internal spin and valley degrees of freedom. The transition between different phases is often identified by the closing of the gap and an enhancement of the conductance. We formulate a criterion for the existence of robust conducting edge states at domain walls between different phases. For example, for a spontaneously layer polarized state at filling factor nu = 2, domains walls between of regions of opposite polarization carry conducting edge modes. A microscopic analysis shows that lattice-scale interactions can favour such a layer polarized state in an intermediate range of magnetic field. We analyze the experiments of Weitz et. al. (Science, 2010) in light of these results. |
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| Spectral and entanglement properties of the bosonic Haldane insulator Ejima, Satoshi (Ernst-Moritz-Arndt University Greifswald, Institute of Physics, Greifswald, Germany) |
| We discuss the existence of a nontrivial topological phase in one-dimensional interacting systems described by the extended Bose-Hubbard model with a mean filling of one boson per site. Performing large-scale density-matrix renormalization group calculations we show that the presence of nearest-neighbor repulsion enriches the ground-state phase diagram of the paradigmatic Bose-Hubbard model by stabilizing a novel gapped insulating state, the so-called Haldane insulator, which, embedded into superfluid, Mott insulator and density wave phases, is protected by lattice inversion symmetry. The quantum phase transition points between the different insulating phases were determined from the central charge, extracted from the von Neumann entropy, and corroborate the universality classes predicted by field theory. Unlike the Mott and density-wave phases, the Haldane phase reveals a characteristic four-fold degeneracy of the entanglement spectrum. We finally demonstrate that the intensity maximum of the dynamical charge structure factor, accessible by Bragg spectroscopy, features the gapped dispersion known from the spin-1 Heisenberg chain. |
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| Symmetry protection of disordered phases and phase transitions in spin ladders Fuji, Yohei (University of Tokyo, Institute for Solid State Physics, Kashiwa, Japan) |
| We investigate gapped phases which retain the full symmetry of the Hamiltonian in $N$-leg spin-1/2 ladders. Based on an effective field theory which has been derived from Abelian bosonization by Schulz, we clarify a distinction between the Haldane phases with odd- and even-integer $N/2$; the former is regarded as a symmetry protected topological (SPT) phase whereas the latter is a topologically trivial phase adiabatically connected with some direct product state. This approach is further applied to various valence bond solid phases such as the rung-singlet, large-D, intermediate-D, and dimer phases. Within our effective field theory, we show that those phases are distinguished by some quantum phase transition under a certain set of symmetries: time reversal, bond-centered inversion, and $pi$ rotations around two spin orthogonal axes. This is consistent with the recent classifications of SPT phases based on the matrix product state and the projective representation of the symmetry group. We also propose another possibility of the phase transition which separates two trivial phases under a combined symmetry of a $pi$ rotation around one spin axis and the site-centered inversion. We demonstrate it on a spin-1 chain with a staggered magnetic field by numerical and perturbative approaches. |
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| Floquet Fractional Chern Insulators Grushin, Adolfo González (Max Planck Institute for the Physics of Complex Systems (MPIPKS), Max Planck Institute for the Physics of Complex Systems, Condensed Matter, Dresden, Germany) |
| We show theoretically that periodically driven systems with short range Hubbard interactions offer a feasible platform to experimentally realize fractional Chern insulator states. We exemplify the procedure for both the driven honeycomb and the square lattice, where we derive the effective steady state band structure of the driven system by using the Floquet theory and subsequently study the interacting system with exact numerical diagonalization. The fractional Chern insulator state equivalent to the 1/3 Laughlin state appears at 7/12 total filling (1/6 filling of the upper band). The state also features spontaneous ferromagnetism and is thus an example of the spontaneous breaking of a continuous symmetry along with a topological phase transition. We discuss light-driven graphene and shaken optical lattices as possible experimental systems that can realize such a state. |
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| DMRG study on topological spin liquid and their phase transition He, Yin-Chen (Max Planck Institute for the Physics of Complex Systems, Condensed matter, Dresden, Germany) |
| We develop the density matrix renormalization group approach to systematically obtain different topological sectors of the spin liquid on an infinite cylinder. As an application, we study the anisotropic kagome Heisenberg model known for hosting a Z2 QSL. We obtain the complete set of four topological degenerate ground states distinguished by the presence or absence of the spinon and vison quasiparticle line, which fully characterizes the topological nature of the quantum phase. We also find a chiral spin liquid phase, which has two topological degenerate ground states and spontaneous time-reversal symmetry breaking. Furthermore, we study the nearest neighbor kagome Heisenberg model, but only two topological sectors have been identified. We have discussed the phase transition from the chiral spin liquid to nearest neighbor kagome Heisenberg model. [1] Obtaining topological degenerate ground states by the density matrix renormalization group by Yin-Chen He, D. N. Sheng, Yan Chen Phys. Rev. B 89, 075110 (2014) [2] Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model by Yin-Chen He, D. N. Sheng, Yan Chen Phys. Rev. Lett. 112, 137202 (2014) [3] Double-semion, Z$_2$, Chiral Spin Liquids and their Transitions in Kagome Antiferromagnets Yin-Chen He and Yan Chen, in preparation |
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| Multi-layer Fractional Quantum Hall States in Lattice Systems Hormozi, Layla (National University of Ireland - Maynooth (NUIM), Mathematical Physics, Maynooth, Ireland) |
| We study fractional quantum Hall states of interacting particles in lattice systems subject to external magnetic fields. When the number of flux quanta per lattice plaquette is close to a rational fraction, the lowest energy states can be mapped to degenerate lowest Landau levels in the continuum, where particles carry an extra degree of freedom -- a pseudospin or layer-index. We find a class of multi-layer fractional quantum Hall states that can form in these systems for bosons with short range interactions and show that topological and spectral properties of these states can be derived from different conformal field theories that are related by a condensation/orbifolding mechanism. |
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| Classification of Topologically ordered Phases Huang, Ching-Yu ( Max Planck Institute for the Physics of Complex Systems, Max Planck Institute for the Physics of Complex Systems, Dresden, Germany) |
| Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of topologically degenerate ground state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a string order parameter can be measured to detect SET. The selection rules will get a characterization of SET. This way is more physical, and can be used by other methods, e.g., quantum Monte Carlo methods or potentially measured experimentally. We demonstrated the usefulness of this approach by considering a spin-1 model on the honeycomb lattice and the resonating valence bond state on a kagome lattice. |
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| Interacting and fractional topological insulators via the Z_2 chiral anomaly Koch-Janusz, Maciej (Weizmann Institute of Science, Weizmann Institute of Science, Condensed Matter Physics, Israel) |
| Recently it was shown that the topological properties of 2D and 3D topological insulators are captured by a $Z_2$ chiral anomaly in the boundary field theory. It remained, however, unclear whether the anomaly survives electron-electron interactions. We show that this is indeed the case, thereby providing an alternative formalism for treating topological insulators in the interacting regime. We apply this formalism to fractional topological insulators (FTI) via projective/parton constructions and use it to test the robustness of all fractional topological insulators which can be described in this way. The stability criterion we develop is easy to check and based on the pairswitching behaviour of the noninteracting partons. In particular, we find that FTIs based on bosonic Laughlin states and the M=0 bosonic Read-Rezayi states are fragile and may have a completely gapped and non-degenerate edge spectrum in each topological sector. In contrast, the $Z_k$ Read-Rezayi states with M=1 and odd k and the bosonic 3D topological insulator with a π/4 fractional theta-term are topologically stable. |
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| Constructing exactly solvable spin models with given critical points from condensate-induced transitions Lahtinen, Ville (University of Amsterdam, Institute of Physics, Physics, Amsterdam, Netherlands) |
| We argue that condensate-induced transitions between gapped two-dimensional topological phases provide a general framework for relating also one-dimensional spin chains at their critical points. The connection is based on the low-energy theories of both systems being described by a conformal field theory (CFT). In topologically ordered phases the possible bulk quasiparticles are in one-to-one correspondence with the primary fields of the CFT describing the edge, while the spectrum of a spin chain at a critical point is always given by some CFT. We argue that a phase transition induced by condensing bulk quasiparticles has a precise counterpart in one-dimensional spin chains in terms of confined boundary conditions. We apply this insight to construct a hierarchy of N-local, but exactly solvable spin-1/2 chains with so(N)_1 critical points. For odd N our models generalize the transverse field Ising chain, the simplest model in our hierarchy. For even N the models can be viewed as longer ranger generalizations of the XY chain, the next model in the hierarchy. The N=3 case provides the first example of a so(3)_1 ≈ su(2)_2 critical point in a local spin-1/2 chain. |
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| Topology and Criticality in Resonating AKLT-loop Spin Liquid States Li, Wei (Ludwig-Maximilians-Universität München, Arnold Sommerfeld Center for Theoretical Physics, Physics department, LMU Munich, Munich, Germany) |
| We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating AKLT-loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional (2D) lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a $mathbb{Z}_2$ spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond (RVB) state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS. |
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| Responses of a topological superconducting wire to the static and dynamic perturbation Maksymenko, Mykola (Max Planck Institute for the Physics of Complex Systems (MPIPKS), Max Planck Institute for the Physics of Complex Systems, Condensed Matter, Dresden, Germany) |
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| Numerical study of a transition between Z2 topologically ordered phases Morampudi, Siddhardh (Max Planck Institute for Physics of Complex Systems, Dresden, Germany) |
| Distinguishing different topologically ordered phases and characterizing phase transitions between them is a difficult task due to the absence of local order parameters. In this work, we use a combination of analytical and numerical approaches to distinguish two such phases and characterize a phase transition between them. The "toric code" and "double semion" models are simple lattice models exhibiting Z2 topological order. Although both models express the same topological ground state degeneracies and entanglement entropies, they are distinct phases of matter because their emergent quasi-particles obey different statistics. For a 1D model, we tune a phase transition between these two phases and obtain an exact solution to the entire phase diagram, finding a second-order Ising x Ising transition. We then use exact diagonalization to study the 2D case and find indications of a first-order transition. We show that the quasi-particle statistics provides a robust indicator of the distinct topological orders throughout the whole phase diagram. |
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| Phases of spinless fermions on the honeycomb lattice from infinite density matrix renormalization group calculations Motruk, Johannes (Max-Planck-Gesellschaft, Max-Planck-Institut für Physik komplexer Systeme, Condensed Matter, Dresden, Germany) |
| We investigate the phase diagram of spinless fermions on the honeycomb lattice in the pesence of nearest- and next-nearest-neighbor interactions by means of the infinite density renormalization group (iDMRG) algorithm. Wheareas mean field theory calculations for this model have suggested the emergence of an interaction-induced Chern insulator phase, it could not be detected in exact diagonalization (ED). Due to ED being limited to small system sizes, the fate of this phase in the thermodynamic limit still remains unclear. We perform our calculations on an infinitely long cylinder with finite circumference considerably exceeding the system sizes accessible in ED. As a result, we find different charge-ordered phases but no sign of the interaction driven Chern insulator phase in agreement with ED results in the literature. |
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| Exactly Solvable Two-body Hamiltonian for the Coupled Pfaffian State of Two-Component Bosons Möller, Gunnar (University of Cambridge, Theory of Condensed Matter (TCM), Cavendish Laboratory, Cambridge, United Kingdom) |
| We demonstrate that the coupled pfaffian state, first discussed in a recent Letter [Phys.~Rev.~Lett.~{bf 108}, 256809 (2012)], is the exact eigenstate of a Hamiltonian with two-body interactions and pair-tunneling terms. We show that this two-body Hamiltonian generates an effective three-body interaction. We show that the coupled Moore-Read pfaffian state can be thought of as the bosonic equivalent of the Halperin 111-state. We discuss both its collective Goldstone mode -- associated with particle transport between the two components -- and its quasihole excitations [1]. We study the excitation spectrum both numerically and analytically, using trial wave functions as well as a conformal field theory point of view: we provide an exact solution for the ground-state and zero-energy quasihole wave functions of the model. We argue that the system can be thought of as two Josephson coupled superfluids, with independent order parameters for each of the two pseudospin channels. However, low-lying eigenstates bind the phase of the order parameter in both layers, with profound consequences for the excitation spectrum. Formalizing this description in terms of conformal field theory correlators, we show that the low energy (edge) spectrum is fully described by a $U(1)_4times U(1)$ theory. [1] G. Möller, L. Hormozi, J. Slingerland & S. Simon, to be published. |
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| Fractional quantum Hall states in lattices and physical implementation Nielsen, Anne Ersbak Bang (Max-Planck-Institut für Quantenoptik, Garching, Germany) |
| We propose an approach based on conformal field theory to build models of spin systems, for which both the Hamiltonians and the ground states are known analytically. We use the method to construct a family of lattice Laughlin states with filling factor $1/q$, and we show that the topological properties of the lattice states are the same as those of the Laughlin states in the continuum. By adding an extra parameter in the wave functions, we can interpolate between the lattice and the continuum states, and we find that the topological entanglement entropy remains the same along the interpolation. The lattice Hamiltonians contain two- and three-body terms, and for $q=2$ we propose a scheme to implement the model in ultracold fermions in optical lattices. The approach can also be used to construct models with more complicated lattice fractional quantum Hall states. References: Nat. Commun. 4, 2864 (2013); New J. Phys. 16, 033025 (2014); J. Stat. Mech. P11014 (2011). |
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| MERA for Spin Chains with Symmetry-Protected Topological Order O'Brien, Aroon (University of Sydney, Australian Research Council of Excellence for Engineered Quantum Systems, School of Physics, Sydney, Australia) |
| We use the multiscale entanglement renormalisation ansatz (MERA) to numerically investigate three critical spin chains with Z2 × Z2 on-site symmetry: a perturbed cluster-state model, a staggered XXZ model and the Ashkin-Teller model. These models all possess a continuous line of criticality at zero temperature, making them ideal candidates for a MERA study [1]. The first two models each possess a phase with symmetry protected topological order (SPTO) for the Z2 x Z2 symmetry group, and are related to each other through a local symmetry-respecting unitary transformation. The Ashkin-Teller model, in contrast, has conventional (non-topological) phases, and can be related to the others through a nonlocal symmetry-respecting unitary transformation when defined on chains with open boundary conditions. Aside from these models exhibiting SPTO, they are also of particular interest due to their connection to measurement-based quantum computation [2]. Our numerics using MERA allow us to extract conformal data for each model, in particular, explicitly incorporating the Z2 × Z2 symmetry in our MERA simulation, nonlocal scaling operators can be extracted. We are able to find qualitative agreement between the numeric results with the predictions from the relevant CFTs in each case. [1] G. Evenbly and G. Vidal, Phys. Rev. B 79, 144108 (2009) [2] A. Doherty and S. Bartlett, Phys. Rev. Lett. 103, 020506 (2009) |
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| Supersolidity hierarchy of spin-1/2 bosons in a triangular lattice Ralko, Arnaud (University Joseph Fourier - CNRS, Institut NEEL, MCBT, Grenoble, France) |
| We study the ground state properties of a frustrated two-species mixture of hard-core bosons on a triangular optical lattice, as a function of tunable amplitudes for tunnelling and interactions. By combining four different methods (a self-consistent cluster mean- field, exact diagonalizations, quantum Monte-Carlo and effective theories), we unravel a very rich and complex phase diagram driven by the frustration and the interplay of the density and spin degrees of freedom. More specifically, we discuss the existence of three original mixture supersolids [1]: (i) a commensurate with frozen densities and supersolidity in spin degrees of freedom, analogous of its fermionic counterpart the pinball phase, in a regime of strong interspecies interactions; and (ii) when this interaction is weaker, two mutually competing incommensurate super solids. Finally, we show how these phases can be stabilized by a quantum fluctuation enhancement of peculiar insulating parent states and we discuss the role of a Rashba-like synthetic spin-orbit coupling, experimentally reachable in optical lattices, on these various phases [2]. [1] Phys. Rev. B 89, 085104 (2014) [2] In preparation (2014) |
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| The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus Repellin, Cecile (Ecole Normale Superieure, Laboratoire Pierre Aigrain - ENS, Physique, Paris, France) |
| We analyze the collective magneto-roton excitations of bosonic Laughlin $nu=1/2$ fractional quantum Hall (FQH) states on the torus and of their analog on the lattice, the fractional Chern insulators (FCIs). We show that, by applying the appropriate mapping of momentum quantum numbers between the two systems, the magneto-roton mode can be identified in FCIs and that it contains the same number of states as in the FQH case. Further, we numerically test the single mode approximation to the magneto-roton mode for both the FQH and FCI case. This proves particularly challenging for the FCI, because its eigenstates have a lower translational symmetry than the FQH states. In spite of this, we construct the FCI single-mode approximation such that it carries the same momenta as the FQH states, allowing for a direct comparison between the two systems. We show that the single-mode approximation captures well a dispersive subset of the magneto-roton excitations both for the FQH and the FCI case. We find remarkable quantitative agreement between the two systems. For example, the many-body excitation gap extrapolates to almost the same value in the thermodynamic limit. |
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| Reentrant topological phase transitions and density of states in a disordered spinless superconducting wire Rieder, Maria-Theresa (Freie Universität Berlin, Institut für Theoretische Physik, Dahlem Center for Complex Quantum Systems, Berlin, Germany) |
| In a one-dimensional spinless p-wave superconductor with coherence length xi, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean free path l = xi/2. We show that a multichannel spinless p-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number N. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean free path l = xi/(N + 1), parametrically smaller than the critical mean free path in one dimension. Our result is valid in the limit that the wire width W is much smaller than the superconducting coherence length xi. |
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| Disentanglers for SPT phases. Ringel, Zohar (Oxford University, University of Oxford, Rudolf Peierls Centre for Theoretical Physics, Oxford, United Kingdom) |
| In the Haldane chain and in the IQHE there is no local order parameter. Notwithstanding a non-local unitary transformation (Disentangler) reveals a hidden order parameter. For the former case the transformation is known as the Kennedy-Tasaki transformation where in latter it is the flux attachment. In both cases the transformed Hamiltonian could be treated using the tools developed for broken symmetry phases. In this talk we discuss how to extend the notion of disentanglers to various Bosonic symmetry protected topological phases using a group-cohomology approach. |
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| Weak coupling instabilities in strained graphene: theory of competing magnetic, topological, and charge-density wave orders. Roy, Bitan (Condensed-Matter Theory Group, CMTC, University of Maryland, Physics, College Park, USA) |
| Remarkable flexibility of quasi-two dimensional graphene membrane, allows an electro-mechanical coupling of the low energy Dirac fermions with a time-reversal symmetric axial magnetic field. Thus when graphene is deliberately strained, the axial/pseudo magnetic field brings a finite number of states near the Dirac point, which, however, live on two different sublattices in the bulk and near the boundary of the system and can be conducive for various orderings at weak interactions. In this talk first I will show that the sublattice degeneracy of the zero energy subband can be lifted by weak nearest-neighbor repulsion by forming a charge-density-wave order, which causes a density imbalance between the bulk and boundary, and competes with the topological quantum anomalous and spin Hall insulators. While the topological orders can be supported by the second-neighbor repulsion among the fermions, a weak onsite Hubbard interaction gives rise to an unconventional magnetic ground state, which despite of locally supporting ferromagnetic order, globally leads to only an antiferromagnet ground state by developing two ferromagnet domains in the bulk and near the edge of the system of exactly opposite magnetization. I will then argue that possibly the onsite repulsion leads to the dominant instability at the Dirac point, whereas the remaining orders can lead to various weak interaction driven fine structure splitting of the remaining zero subband. Finally, a global phase diagram of the ordered phases in strained graphene will be presented, and possibility of simultaneous coexistence of multiple orders will be addressed. |
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| Tunnel Magentoresistance scan of a pristine 3D topological insulators surfaces Roy, Sthitadhi (Max Planck Gesellschaft, Max Planck Institute for the Physics of Complex Systems, Condensed Matter, Dresden, Germany) |
| Though Fermi-surface of surface states of 3D topological insulator (TI) has zero magnetisation but multi terminal geometry can induce a finite magneto resistance response consistent with the type of spin-momentum locking in hand. We propose a multi-terminal set up which directly couples to the local (in momentum space) magnetisation hence leading to a finite tunnel magnetoresistance (TMR) for the non-magnetic TI surface states, when coupled to a spin polarised STM probe. This multi-terminal TMR not only provides an unique signature of spin-momentum locking for a pristine TI but also provides direct measure of momentum resolved out of plane polarisation of hexagonally warped Fermi surfaces relevant for $Bi_2Te_3$ which could be as comprehensive as spin resolved ARPES. |
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| Probing Topological nature of many body ground state for a system of particles on a kagome lattice at fractional fillings Roychowdhury, Krishanu (MPIPKS, Condensed Matter, Dresden, Germany) |
| System of particles (fermions and bosons) on a frustrated lattice like kagome can support interesting phases at fractional filling. In a recent work, we showed that interplay between spin and charge degrees of freedoms of the strongly correlated fermions at 2/3 filling can host charge ordered phase as well as resonating plaquette phase with a quantum phase transition between them driven by spin fluctuations. However, the interaction term is restricted to nearest neighbors only. Given the condition relaxed i.e. allowing longer range interaction, the system is expected to stabilize Z_2 topological phases at different fractional fillings like 1/6, 1/3 and 1/2. A smooth connection between different fillings is also presented in terms of the emerging Z_2 structure of the underlying gauge theory. |
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| Topological states in a one-dimensional Fermi gas with attractive interactions Ruhman, Jonathan (Weizmann Institute of Science, Weizmann Institute of Science, Condensed matter , Rehovot, Israel) |
| We consider a one-dimensional Fermi gas with Rashba spin-orbit coupling, a Zeeman field and attractive interactions. In spite of particle number conservation and the absence of a single particle gap we show that protected ground state degeneracy emerges when the topological region is placed in between two trivial one-dimensional superconductors. Unlike the realization of topological superconductivity in proximity coupled wires the Majorana modes carry only the quantum number associated with the total spin parity and are delocalized over the whole topological region. The two degenerate states of the q-bit correspond to an even or odd number of spins in the middle region. However, switching between these two states can only be achieved by adding or removing an odd number of fermions in topological region with a finite charging energy cost. To avoid the charging energy one needs two topological regions which can interchange spins amongst themselves without passing any charge. We also discuss the effect of phase slips in the trivial regions which couple to the spin parity of the topological region and cause a splitting of the degeneracy which scales as (1/L)^(K/2) where K is the Luttinger parameter. |
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| Topological order and symmetries in tensor network models Schuch, Norbert (RWTH Aachen University, JARA Institute for Quantum Information, Aachen, Germany) |
| Tensor network states provide a local description of strongly correlated quantum states, and allow for the efficient description of both non-chiral and chiral topologically ordered states. In this talk, I will discuss how topological order can be understood from local symmetries in the tensor network representation of a model, which yield a comprehensive explanation of the topological features displayed by the system such as ground space degeneracy, anyonic excitations, or protected edge physics. I will also discuss how the behavior of the system relative to its symmetries gives rise to topological phase transitions, as well as the way in which similar symmetries show up in chiral topological models where they can serve as a guideline for the construction of new chiral tensor network models. |
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| Many-body localization and entanglement in disordered quantum spin models Singh, Rajeev (Max Planck Institute for the Physics of Complex Systems, Max Planck Institute for the Physics of Complex Systems, Condensed Matter Physics, Dresden, Germany) |
| The presence of disorder in a non-interacting system can localize all the energy eigenstates, a phenomena dubbed Anderson localization. Many-body localization is a generalization of this phenomena to include interactions. The dynamics of disordered interacting quantum systems shows a logarithmic growth (associated with glassy systems) in the entanglement entropy after a global quench [1]. For finite systems, this growth saturates and the saturation value obeys a volume law. A volume law leads to a constant entanglement entropy per site which might be related to thermal entropy and imply partial thermalization of the system. In this work, we study further the dynamics of disordered quantum spin systems and parameter dependence of the long time saturation. [1] J. H. Bardarson, F. Pollmann and J. E. Moore, Phys. Rev. Lett. 109, 107202 (2012). |
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| Two leg bosonic ladder in an external magnetic field at unit filling Sterdyniak, Antoine (Universität Innsbruck, Institut für Theoretische Physik, Innsbruck, Austria) |
| Motivated by the recent experimental realizations of artificial gauge field on optical lattices, we study the two-leg bosonic ladder in an external magnetic field, both analytically using bozonization techniques and numerically using finite size density matrix renormalization group algorithm. At unit filling, interacting bosons can exhibit a rich variety of phases on ladders. At large interaction, they form a Mott insulator phase while, at smaller interaction, they exhibit a Meissner phase and, more intriguing floating and staggered vortex phases. A weak chiral Mott insulator phase was also found previously for intermediate interaction strength. We determine the phase diagram and Luttinger parameters from correlations functions and entanglement spectrum. While usually thought to be second order, some of the phase transitions appear to be first order. |
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| Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling Varjas, Daniel (UC Berkeley, Physics, Berkeley, USA) |
| We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension. |
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