Research areas

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In the Condensed Matter Division we are interested in a broad range of collective phenomena. These can be grouped under three central umbrellas of quantum matter, new kinds of order and quantum dynamics, while still substantial interconnections naturally emerge, see the illustration in the figure above.

A key scope of research is the identification and theoretical description of new kinds of order ranging from unconventional phases such as quantum spin liquids appearing in frustrated magnets to topological matter. These phases often cannot be described by local order parameters but rather entail peculiar entanglement properties linking condensed matter theory directly to quantum information concepts.

The far from equilibrium regime on the other hand, nowadays experimentally accessible in so-called quantum simulators, naturally provides the room for novel quantum states because constraints by equilibrium principles such as the equal a priori probability in the microcanonical ensemble are lifted generically. Prominent examples include the many-body localized phase or eigenstate phases in periodically driven Floquet systems such as discrete time crystals. Detailed descriptions of the individual research topics can be found under the respective embedded links in the figure above.



The Kibble-Zurek mechanism at exceptional points
Balazs Dora, Markus Heyl, Roderich Moessner

Exceptional points (EPs) are ubiquitous in non-Hermitian systems, and represent the complex counterpart of critical points. By driving a system through a critical point at finite rate induces defects, described by the Kibble-Zurek mechanism, which finds applications in diverse fields of physics. Here we generalize this to a ramp across an EP. We find that adiabatic time evolution brings the system into an eigenstate of the final non-Hermitian Hamiltonian and demonstrate that for a variety of drives through an EP, the defect density scales as τ-(d + z)ν/(zν + 1) in terms of the usual critical exponents and 1/τ the speed of the drive. Defect production is suppressed compared to the conventional Hermitian case as the defect state can decay back to the ground state close to the EP. We provide a physical picture for the studied dynamics through a mapping onto a Lindblad master equation with an additionally imposed continuous measurement.

Nat. Commun. 10, 2254 (2019)




Topological superconductivity in a phase-controlled Josephson junction
H. Ren, F. Pientka, S. Hart, A. T. Pierce, M. Kosowsky, L. Lunczer, R. Schlereth, B. Scharf, E. M. Hankiewicz, L. W. Molenkamp, B. I. Halperin, and A. Yacoby

Topological superconductors can support localized Majorana states at their boundaries1,2,3,4,5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8,9,10,11,12,13,14,15,16,17,18,19,20,21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

Nature 569, 93 (2019)





Efficiently solving the dynamics of many-body localized systems at strong disorder
Giuseppe De Tomasi, Frank Pollmann, Markus Heyl

We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the time evolution with a polynomial effort in system size and independent of the desired time scales. We use our method to study quantum information propagation, correlation functions, and temporal fluctuations in one- and two-dimensional many- body localization systems. Moreover, we outline strategies for a further systematic improvement of the accuracy and we point out relations of our method to recent attempts to simulate the time dynamics of quantum many-body systems in classical or artificial neural networks.

Phys. Rev. B 99, 241114 (2019)




Dynamical Structure Factor of the Three-Dimensional Quantum Spin Liquid Candidate NaCaNi2F7
S. Zhang, H. J. Changlani, K. W. Plumb, O. Tchernyshyov, and R. Moessner

We study the dynamical structure factor of the spin-1 pyrochlore material NaCaNi2F7, which is well described by a weakly perturbed nearest-neighbour Heisenberg Hamiltonian, Our three approaches-molecular dynamics simulations, stochastic dynamical theory, and linear spin wave theory-reproduce remarkably well the momentum dependence of the experimental inelastic neutron scattering intensity as well as its energy dependence with the exception of the lowest energies. We discuss two surprising aspects and their implications for quantum spin liquids in general: the complete lack of sharp quasiparticle excitations in momentum space and the success of the linear spin wave theory in a regime where it would be expected to fail for several reasons.

Phys. Rev. Lett. 122, 167203 (2019)





Avoided quasiparticle decay from strong quantum interactions
Ruben Verresen, Roderich Moessner, Frank Pollmann

Quantum states of matter-such as solids, magnets and topological phases-typically exhibit collective excitations (for example, phonons, magnons and anyons)1. These involve the motion of many particles in the system, yet, remarkably, act like a single emergent entity-a quasiparticle. Known to be long lived at the lowest energies, quasiparticles are expected to become unstable when encountering the inevitable continuum of many-particle excited states at high energies, where decay is kinematically allowed. Although this is correct for weak interactions, we show that strong interactions generically stabilize quasiparticles by pushing them out of the continuum. This general mechanism is straightforwardly illustrated in an exactly solvable model. Using state-of-the-art numerics, we find it at work in the spin- 1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF). This is surprising given the expectation of magnon decay in this paradigmatic frustrated magnet. Turning to existing experimental data, we identify the detailed phenomenology of avoided decay in the TLHAF material2 Ba3CoSb2O9, and even in liquid helium3,4,5,6,7,8, one of the earliest instances of quasiparticle decay9. Our work unifies various phenomena above the universal low-energy regime in a comprehensive description. This broadens our window of understanding of many- body excitations, and provides a new perspective for controlling and stabilizing quantum matter in the strongly interacting regime.

Nature Physics (2019)




Quantum localization bounds Trotter errors in digital quantum simulation
Markus Heyl, Philipp Hauke, and Peter Zoller

A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization- by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time. DQS is thus intrinsically much more robust than suggested by known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size, which separates a localized region with controllable Trotter errors from a quantum chaotic regime. Our findings show that DQS with comparatively large Trotter steps can retain controlled errors for local observables. It is thus possible to reduce the number of gate operations required to represent the desired time evolution faithfully.

Sci. Adv. 5, eaau8342 (2019)