# Anderson Localization and Interactions

For each poster contribution there will be one poster wall (width: 97 cm, height: 250 cm) available. Please do not feel obliged to fill the whole space. Posters can be put up for the full duration of the event.

### Superconductor-Insulator Transition in disordered Josephson junction chains

Bard, Matthias

Starting from a lattice model for Josephson junction chains that includes capacitive couplings to the ground as well junction capacitances, we derive the effective low-energy field theory. Quantum phase slips lead to the suppression of the superconducting correlations and drive the transition to the insulating state. Stray charges are a very important source of disorder in theses systems, which suppress the coherence of phase slips. In this way they facilitate superconducting correlations. With the help of the renormalization group, we obtain the phase diagram and evaluate the temperature dependence of the dc conductivity and system-size dependence of the resistance around the superconductor-insulator transition. The interplay of superconductivity and disorder results in a strongly nonmonotonic behavior of these quantities.

### Spin transport and filtering in the presence of disorder

Benini, Leonardo

We theoretically investigate a simple tight binding Hamiltonian to understand the stability or robustness of spin polarized transport of particles with arbitrary spin state, in presence of disorder. The projectile with a general spin state is made to pass through a linear chain of magnetic atoms. Depending on the spin of the projectile, the chain of magnetic atoms unravels a hidden transverse dimensionality that can be exploited to engineer the energy regimes which allow one particular spin state. In depth numerical analysis is carried out to understand the roles played by the spin projections in different regimes of the densities of states through the introduction of a spin-resolved projected localization length with random, uncorrelated disorder in the potential profile offered by the magnetic substrate and/or in the orientations of the magnetic moments with respect to a given direction in space.

### Spin echoes in disordered Hubbard models

We study spin-echo signals in disordered Hubbard models. We show that the spin echo signal is characterized by a timescale which depends non-monotonically on disorder strength through the many-body localization transition. Our results yield a tool for detecting the transition which is based on short time evolution, making it efficient numerically and an attractive tool for experimental implementation.

### Generalized Wigner-Dyson level statistics and many-body localization

Buijsman, Wouter

The study of level statistics is of unambiguous importance in the characterization of crossovers between thermal and localized phases. We study the level statistics of a paradigmatic model in the field of many-body localization. We report near-perfect agreement with the eigenvalue statistics of the Gaussian $\beta$ ensemble in both the thermal, localized, and intermediate regime. We argue that the eigenvalue statistics of this ensemble, covering both Poissonian ($\beta \to 0$) and Wigner-Dyson statistics ($\beta = 1,2,4$), can be naturally interpreted as generalized Wigner-Dyson statistics. URL: https://staff.science.uva.nl/w.buijsman/dresden.

### Duality in power-law localization in disordered one-dimensional systems

Deng, Xiaolong

The transport of excitations between pinned particles in many physical systems may be mapped to single-particle models with power-law hopping, 1/r^a. For randomly spaced particles, these models present an effective peculiar disorder that leads to surprising localization properties. We show that in one-dimensional systems almost all eigenstates (except for a few states close to the ground state) are power-law localized for any value of a>0. Moreover, we show that our model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops (a<1) and short-range hops (a>1) in which the wave function amplitude falls off algebraically with the same power γ from the localization center.

### Boundary-driven Heisenberg chain in the long-range interacting regime: Robustness against far-from-equilibrium effects

Droenner, Leon

The disordered Heisenberg spin-chain has achieved the role of a standard model when studying localization in the presence of interactions, called many-body localization (MBL). We investigate the transport properties of this model and compare it to a long-range interacting scenario. By applying two magnetic boundary reservoirs, we drive the system out of equilibrium and induce a nonzero steady-state current [1]. We are in particular investigating the far-from equilibrium situation for a strong external bias (i.e. left reservoir contains only spin up magnetization and the right reservoir only spin down). The common isotropic nearest-neighbor coupling shows negative differential conductivity and a transition from diffusive to subdiffusive transport for a far-from-equilibrium driving. This results in subdiffusive transport already for zero disorder. In contrast, the long-range coupled chain shows nearly ballistic transport and linear response for all potential differences and coupling strengths of the external reservoirs. When turning on disorder, the change in the transport to subdiffusive transport results purely from disorder (i.e. Griffiths effects) and is independent of the investigated external reservoir parameters [2]. Therefore, to distinguish many-body localization as an effect of disorder from the spin-blockade, long-range coupling provides a clear understanding of MBL for boundary-driven systems as it is robust against far-from-equilibrium effects. [1] M. Znidaric et al, Phys. Rev. Lett. 117, 040601 (2016). [2] L. Droenner and A. Carmele Phys. Rev. B 96, 184421 (2017).

### Vortex-antivortex pairs in planar Josephson junction arrays: instabilities and interactions

Estellés Duart, Francisco

Proliferation of topological defects like vortices and dislocations plays a key role in the physics of systems with long-range order. Topological defects are characterized by their topological charge reflecting fundamental symmetries and conservation laws of the system. Conservation of topological charge manifests itself in extreme stability of static topological defects because destruction of a single defect requires overcoming a huge energy barrier proportional to the system size. However, the stability of driven topological defects remains largely unexplored. Here we address this issue and investigate numerically a dynamic instability of moving vortices in planar arrays of Josephson junctions. We show that a single vortex driven by sufficiently strong current becomes unstable and destroys superconductivity by triggering a chain reaction of self-replicating vortex-antivortex pairs forming linear of branching expanding patterns.

### Construction of exact constants of motion and effective models for many-body localized systems

Goihl, Marcel

One of the defining features of many-body localization is the presence of extensively many quasi-local conserved quantities. These constants of motion constitute a corner-stone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasi-local unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish a new approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.

### Analytically solvable renormalization group for the many-body localization transition

Goremykina, Anna

We introduce a simple, exactly solvable strong-randomness renormalization group (RG) model for the many-body localization (MBL) transition in one dimension. Our approach relies on a family of RG flows parametrized by the asymmetry between thermal and localized phases. We identify the physical MBL transition in the limit of maximal asymmetry, reflecting the instability of MBL against rare thermal inclusions. We find a critical point that is localized with power-law distributed thermal inclusions. The typical size of critical inclusions remains finite at the transition, while the average size is logarithmically diverging. We propose a two-parameter scaling theory for the many-body localization transition that falls into the Kosterlitz-Thouless universality class, with the MBL phase corresponding to a stable line of fixed points with multifractal behavior.

### Multifractality at the spin quantum Hall transition revisited

Hernangomez Perez, Daniel

Recent analytical work predicts the multifractal spectrum of the integer quantum Hall (IQH) transition (class A) to be exactly parabolic [1]. The available numerical studies of the spectrum [2,3,4] suggested otherwise, but they are inconclusive, since they have not taken into account finite size corrections due to irrelevant scaling variables. These corrections are known to be very important for the precise determination of the localization length exponent at the IQH transition [5, 6]. As compared to the IQH transition, the spin quantum Hall (SQH) transition appears to be under much better control, numerically, partially because the corrections to scaling seem small. Motivated by the preceding observations, we here present a numerical study of wavefunction statistics for the SQH within the framework of Chalker-Coddington network models. The spectrum we obtain obeys the symmetry relation derived in [7]; the analytically known exponents for wavefunction moments q = 2,3 obtained numerically: -0.2505 +/- 0.003, -0.749 +/-0.002. The spectrum is not, however, parabolic. Our research thus sets a consistency check for analytical theories of the SQH. Finally, we will also report results for the scaling of moments of wavefunction determinants [8]. The latter are associated with an independent, subleading set of multifractal exponents, which we calculated. [1] R. Bondesan, D. Wieczorek, and M. R. Zirnbauer, Nucl. Phys. B 918, 52 (2017). [2] R. Bondesan, D. Wieczorek, and M. R. Zirnbauer, Phys. Rev. Lett. 112, 186803 (2014). [3] F. Evers, A. Mildenberger, and A. D. Mirlin, Phys. Rev. Lett. 101, 116803 (2008). [4] H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, Phys. Rev. Lett. 101, 116802 (2008). [5] K. Slevin and T. Ohtsuki, Phys. Re.b B 80, 041304 (2009). [6] H. Obuse, A. R. Subramaniam, A. Furusaki, I. A. Gruzberg, and A. W. W. Ludwig, Phys. Rev. B 82, 035309 (2010). [7] A. Gruzberg, A. W. W. Ludwig, A. D. Mirlin, and M. Zirnbauer, Phys. Rev. Lett. 107, 086403(2011). [8] I. Gruzberg, A. D. Mirlin, and M. Zirnbauer, Phys. Rev. B 87, 125114 (2013).

### Entanglement clusters through the many-body localization phase transition

Herviou, Loic

We study numerically the formation of entanglement clusters across the many-body localization phase transition. We observe a crossover between strong many-body entanglement in the ergodic phase to weak local correlations in the localized phase, with contiguous clusters throughout the phase diagram. Critical states close to the transition have a structure compatible with fractal or multiscale-entangled Griffith states, characterized by entanglement at multiple levels: small strongly entangled clusters are weakly entangled together to form larger clusters. The critical point therefore features subthermal entanglement and a power-law distributed cluster size, while the localized phase presents an exponentially decreasing distribution. These results are consistent with some of the recently proposed phenomenological renormalization-group schemes characterizing the many-body localized critical point, and may serve to constrain other such schemes.

### Detection and characterization of Many-Body Localization in Central Spin Models

Hetterich, Daniel

We analyze a disordered central spin model, where a central spin interacts equally with each spin in a periodic one dimensional random-field Heisenberg chain. If the Heisenberg chain is initially in the many-body localized (MBL) phase, we find that the coupling to the central spin suffices to delocalize the chain for a substantial range of coupling strengths. We calculate the phase diagram of the model and identify the phase boundary between the MBL and ergodic phase. Within the localized phase, the central spin significantly enhances the rate of the logarithmic entanglement growth and its saturation value. We attribute the increase in entanglement entropy to a non-extensive enhancement of magnetization fluctuations induced by the central spin. Finally, we demonstrate that correlation functions of the central spin can be utilized to distinguish between MBL and ergodic phases of the 1D chain. Hence, we propose the use of a central spin as a possible experimental probe to identify the MBL phase.

### Constructing electronic phase diagram for the half-filled Hubbard model with disorder

Hoang, Anh Tuan

The electronic phase diagram of strongly correlated systems with disorder is constructed using the typical-medium theory. For half-filled system, the combination of the linearized dynamical mean field theory and equation of motion approach allows to derive the explicit equations determining the boundary between the correlated metal, Mott insulator, and Anderson insulator phases. Our result is consistent with those obtained by the more sophisticated methods and it demonstrates that the equation of motion approach is a simple, but reliable impurity solver for constructing the diagram phase in the correlated systems with disorder.

### Accessing eigenstate spin-glass order from reduced density matrices

Javanmard, Younes

Many-body localized phases may not only be characterized by their ergodicity breaking, but can also host ordered phases such as the many-body localized spin-glass (MBL-SG). The MBL-SG is challenging to access in a dynamical measurement and therefore experimentally since the conventionally used Edwards-Anderson order parameter is a two-point correlation function in time. In this work, we show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-glass order parameter captures spin-glass phases in random Ising chains both in many-body eigenstates as well as in the nonequilibrium dynamics from a local in time measurement. We discuss how our results can be used to observe MBL-SG order within current experiments in Rydberg atoms and trapped ion systems.

### Interacting Majorana chain in presence of disorder

Karcher, Jonas

We investigate a majorana chain model with potential applications to the description of Kitaev edges. The model exhibits various topological phases which are separated by critical lines. Since the non-interacting system belongs to class BDI one would expect these lines to remain critical in presence of disorder if the interaction is sufficiently weak . Recent numerical studies using DMRG confirm this for attractive interactions. For strong repulsive interactions, these studies find that the system localizes. Our preliminary results show localization also for weak repulsive interaction. We want to understand the mechanism that drives the system into localization despite topological protection. To reach this goal we employ both DMRG calculations and diverse analytical RG-schemes. Our results from DMRG suggest spontaneous breaking of the translation symmetry. This cannot be understood from the weak disorder and weak interaction RG around the clean noninteracting fixed point (FP), where the interaction is irrelevant. Hence we investigate the stability of the infinite randomness FP against weak interaction. The wave functions exhibit (multi)fractality. Correlators are again computed analytically using a SUSY transfer matrix techniques. This approach is augmented by results from exact diagonalization. From their scaling behaviour we want to deduce the interaction RG flow.

### Transport in long-range interacting disordered spin chains

Kloss, Benedikt

We numerically study spin transport and spin-density profiles after an initial spin-quench in disordered XXZ spin-chains with long-range interactions, decaying as a power-law, r^{-\alpha} with distance. The results are obtained with tensor network state methods, which allow to treat systems of large enough size to eliminate finite size effects due to the long-rangedness of the interaction. Despite their limitation to short times due to the growth of entanglement entropy with time, statements about transport could be made in our previous study on clean long-range interacting systems (arXiv:1804.05841).

### Dynamics in the ergodic phase of the many-body localiza- tion transition for a periodically driven system

Lezama Mergold Love, Talía

Closed disordered interacting quantum systems can experience a many-body localization phase transition when tuning the disorder strength around its critical value. Recent studies have shown that the ergodic phase is not a common metallic phase but that it rather exhibits non-trivial mechanisms (mainly Griffiths effects) foregoing the many-body localized phase. Those mechanisms have been described in terms of dynamical quantities such as autocorrelation functions, return probability, entanglement entropy, and imbalance, to mention some. Here, we study the dynamics of a Floquet model of many-body localization, focussing on the dynamical regimes on the ergodic side of the transition.

### SYK model with quadratic perturbations: the route to a non-Fermi-liquid.

Lunkin, Aleksey

Sachdev, Ye and Kitaev model (SYK model) is an exactly solvable example of a fermionic system with extremely strong interaction, as it lacks any quadratic terms in fermionic operators. The SYK model describes a system of N Majorana fermions which randomly interact with each other. In the low-energy limit J and in the limit $N\rightarrow \infty$ the system is described by the saddle-point equations which have a rich group of symmetry: $t \rightarrow f(t)$ where f(t) is an arbitrary monotonic function. At finite large N this reparametrization mode leads to fluctuations controlled by the simple Gaussian action written in terms of phase variable $\phi(t) = ln(df(t)/dt)$. As a result of integration over the $\phi$ mode, the fermionic Green function behaves as $\eps^{1/2}$ at lowest energies $\eps\llJ/N$. This behavior is qualitatively different from the one well-known for Fermi liquid. In our work, we study the stability of the SYK model with respect to a perturbation quadratic in fermionic operators. We develop analytic perturbation theory in the amplitude of the perturbation and demonstrate the stability of the SYK infra-red asymptotic behavior with respect to weak perturbation. Thus we demonstrate explicitly that non-Fermi-liquid behavior can be realized in a finite area of the parameter space characterized by interacting fermionic Hamiltonians.

### Anderson localization of two interacting particles using discrete time quantum walks

Malishava, Merab

We study Anderson localization in a system of two interacting particles (TIP) whose unitary evolution is efficiently emulated with Interacting Discrete-Time Quantum Walks (IDTQW). In a recent work [1] a single particle DTQW with disorder was studied. We use these results and compute the dependence of the size of the TIP wave function on the control parameters of the system. We are in particular interested in the scaling of the TIP localization length with the single particle localization length in the limit of large values of the latter. Two qualitatively different limits have been identified and will be addressed. Due to the efficiency of the unitary IDTQW we will enter scaling regions which were inaccessible by previous Hamiltonian TIP dynamics. [1] I. Vakulchyk, M. V. Fistul, P. Qin, and S. Flach (2017), Phys. Rev. B 96, 144204.

### Weak ergodicity breaking from quantum many-body scars

Michailidis, Alexios

The thermodynamic description of many-particle systems rests on the assumption of ergodicity, the ability of a system to explore all allowed configurations in the phase space. Recent studies on many-body localization have revealed the existence of systems that strongly violate ergodicity in the presence of quenched disorder. Here, we demonstrate that ergodicity can be weakly broken by a different mechanism, arising from the presence of special eigenstates in the many-body spectrum that are reminiscent of quantum scars in chaotic non-interacting systems. In the single-particle case, quantum scars correspond to wavefunctions that concentrate in the vicinity of unstable periodic classical trajectories. We show that many-body scars appear in the Fibonacci chain, a model with a constrained local Hilbert space that has recently been experimentally realized in a Rydberg-atom quantum simulator. The quantum scarred eigenstates are embedded throughout the otherwise thermalizing many-body spectrum but lead to direct experimental signatures, as we show for periodic recurrences that reproduce those observed in the experiment. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, opening up opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable.

### Integer quantum Hall transitions on tight-binding lattices

Puschmann, Martin

Martin Puschmann(1), Philipp Cain(2), Michael Schreiber(2), and Thomas Vojta(1) 1) Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA 2) Institute of Physics, Chemnitz University of Technology, 09107 Chemnitz, Germany Even though the integer quantum Hall transition has been investigated for nearly four decades its critical behavior remains a puzzle. The best theoretical and experimental results for the localization length exponent $\nu$ differ significantly from each other, questioning our fundamental understanding. While this discrepancy is often attributed to long-range Coulomb interactions, Gruzberg et al. [1] recently suggested that the semiclassical Chalker-Coddington (CC) model, widely employed in numerical simulations, is incomplete because it does not contain all types of disorder relevant for the quantum Hall transition. Instead, they presented a geometrically disordered CC model, whose localization length exponent appears to agree better with the experimental measurements. This casts doubt on the central established theoretical results. To shed light on the controversy, we perform a high-accuracy study for a microscopic model of discorded electrons: We investigate the integer quantum Hall transition in the lowest Landau band of two-dimensional tight-binding lattices for non-interacting electrons affected by a perpendicular magnetic field. Specifically, we consider both simple square lattices, where Landau levels are broadened by random potentials, and random Voronoi-Delaunay lattices in which (topological) disorder is introduced by bonds between randomly positioned sites. For the latter, we have recently shown that, in contrast to several classical phase transitions [2], the disorder-induced short-range (anti-)correlation does not lead to qualitative changes in absence of the magnetic field [3]. In the current work, we calculate, based on a recursive Green function approach, the smallest positive Lyapunov exponent describing the long-range behavior of the wave-function intensities along a quasi-one-dimensional lattice strip. In both systems, we find a localization length exponent $\nu\approx 2.60$ in the universal regime, validating the result (see e.g. [4]) of the standard CC network model. This suggests that the regular structure of the CC model is not the culprit causing the discrepancy between the theoretical and the experimental values. Solving the exponent puzzle is still an open task, with the Coulomb interaction being the likeliest outcome. As a byproduct, we investigate within the same framework the topological-disorder-induced localization-delocalization transitions in three-dimensional random Voronoi-Delaunay lattices, yielding results in excellent agreement with studies of conventional systems. [1] I. A. Gruzberg et al., Phys. Rev. B 95, 125414 (2017) [2] H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, 120602 (2014) [3] M. Puschmann et al., Eur. Phys. J. B 88, 314 (2015) [4] K. Slevin and T. Ohtsuki, Phys. Rev. B 80, 041304 (2009)

### Interplay of coherent and dissipative dynamics in condensates of light

Based on the Lindblad master equation approach we obtain a detailed microscopic model of photons in a dye-filled cavity, which features condensation of light. To this end we generalise a recent non-equilibrium approach of Kirton and Keeling such that the dye-mediated contribution to the photon-photon interaction in the light condensate is accessible due to an interplay of coherent and dissipative dynamics. We describe the steady-state properties of the system by analysing the resulting equations of motion of both photonic and matter degrees of freedom. In particular, we discuss the existence of two limiting cases for steady states: photon Bose-Einstein condensate and laser-like. In the former case, we determine the corresponding dimensionless photon-photon interaction strength by relying on realistic experimental data and find a good agreement with previous theoretical estimates. Furthermore, we investigate how the dimensionless interaction strength depends on the respective system parameters.

### Signature of chaos and delocalization in a periodically driven many body system: An out-of-time-order correlation study

Ray, Sayak

In this work we study the out-of-time-order correlation (OTOC) for one-dimensional periodically driven hardcore bosons in the presence of Aubry-Andr\'e (AA) potential and show that both the spectral properties and the saturation values of OTOC in the steady state of these driven systems provide a clear distinction between the many body localized (MBL) and delocalized phases of these models. Our results, obtained via exact numerical diagonalization of these boson chains, thus indicate that OTOC can provide a signature of drive induced delocalization of the MBL states even for systems which do not have a well defined semiclassical (and/or large $N$) limit. We demonstrate the presence of such signature by analyzing two different drive protocols for hardcore boson chains leading to distinct physical phenomena and discuss experiments which can test our theory. Reference : Sayak Ray, Subhasis Sinha and Krishnendu Sengupta, arXiv:1804.01545 (2018).

### Strong disorder in nodal semimetals: Schwinger-Dyson–Ward approach

Sbierski, Björn

The self-consistent Born approximation quantitatively fails to capture disorder effects in semimetals. We present an alternative simple-to-use non-perturbative approach to the disorder induced self-energy. It requires a sufficient broadening of the quasiparticle pole and the solution of a differential equation on the Matsubara axis. We demonstrate the performance of our method for various paradigmatic semimetal Hamiltonians and compare our results to exact numerical reference data. For intermediate and strong disorder, our approach yields quantitatively correct momentum resolved results. It is thus complementary to existing RG treatments of weak disorder in semimetals.

### Energy transport in the driven disordered XYZ

Schulz, Maximilian

We explore the physics of the disordered XYZ spin chain using two complementary numerical techniques: exact diagonalization (ED) on chains of up to 17 spins, and time-evolving block decimation (TEBD) on chains of up to 400 spins. Our principal findings are as follows. First, the clean XYZ spin chain shows ballistic energy transport for all parameter values that we investigated. Second, for weak disorder there is a stable diffusive region that persists up to a critical disorder strength that depends on the XY anisotropy. Third, for disorder strengths above this critical value energy transport becomes increasingly subdiffusive. Fourth, the many-body localization transition moves to significantly higher disorder strengths as the XY anisotropy is increased. We discuss these results, and their relation to our current physical picture of subdiffusion in the approach to many-body localization.

### Transport in systems with nodal degeneracy

Sinner, Andreas

We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo-Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless diffusion modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmic divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near the universal conductivity. We extend our analysis by including effects of anisotropy on hexagonal lattices.

### Multifractality of wave functions on a Cayley tree: From root to leaves

Sonner, Michael

We explore the evolution of wave-function statistics on a finite Bethe lattice (Cayley tree) from the central site ("root") to the boundary ("leaves"). We show that the eigenfunction moments $P_q=N\langle|\Psi(i)|^(2q)\rangle$ exhibit a multifractal scaling $P_q\propto N^{\tau_q}$ with the volume (number of sites) $N$ at $N\to\infty$. The multifractality spectrum $\tau_q$ depends on the strength of disorder and on the parameter s characterizing the position of the observation point i on the lattice. Specifically, $s=r/R$, where $r$ is the distance from the observation point to the root, and $R$ is the “radius” of the lattice. We demonstrate that the exponents $\tau_q$ depend linearly on s and determine the evolution of the spectrum with increasing disorder, from delocalized to the localized phase. Analytical results are obtained for the $n$-orbital model with $n\ggt 1$ that can be mapped onto a supersymmetric $\sigma$ model. These results are supported by numerical simulations (exact diagonalization) of the conventional ($n=1$) Anderson tight-binding model.

### Effects of self-consistency in mean-field theories of disordered systems: Superconductor Insulator Transition

Stosiek, Matthias

Authors: Matthias Stosiek, Ferdinand Evers Our general interest is in aspects of self-consistency with respect to disorder in the mean-field treatment of disordered interacting systems. The example we here consider is the Superconductor-Insulator Transition (SIT), where the superconducting gap is calculated in the presence of short-range disorder. Our focus is on disordered films with conventional s-wave pairing that we study numerically employing the negative-U Hubbard model within the standard Bogoliubov-deGennes approximation. The general question that we would like to address concerns the auto-correlation function of the pairing amplitude: Does it qualitatively change if full self-consistency is accounted for? Our research might have significant impact on the understanding of the SIT, if extra correlations appear due to the self-consistency condition that turn out sufficiently long-ranged. Such correlation effects are ignored in major analytical theories [1,2]. To study the long-range behavior of the order parameter correlations, the treatment of large system sizes is necessary. Due to the self-consistency requirement, the relevant sizes (e.g. $10^6$ sites) are numerically very expensive to achieve. For this reason, we have developed a parallelized code based on the Kernel Polynomial Method (KPM) [3]. We present data that indicates the existence of very long ranged (power-law) correlations that may indeed change the critical behavior in a significant way. Acknowledgements: We express our gratitude to the LRZ for computational support within the project pr53lu and to the DFG for financial support via the DFG projects EV30-8/1, EV30-11/1, EV30-12/1. References: [1] M.V. Feigel’man and L.B. Ioffe, Phys. Rev B 92, 100509(R) (2015). [2] M.V. Feigel’man, L.B. Ioffe, V.E. Kravtsov, E. Cuevas, Ann. Phys. 325, 1390 (2010). [3] A. Weiße, G. Wellein, A. Alvermann, H. Fehske, Rev. Mod. Phys. 78, 275 (2006).

### Spin relaxation in the disordered XXZ chain

Weiner, Felix

We present numerical results for spin relaxation in the XXZ Heisenberg chain with random longitudinal fields, which is one of the prototypical models for the many-body localization transition. We study the time-dependent $S^z$ propagator at high temperatures, which we evaluate by means of matrix product operator techniques as well as exact Chebyshev time propagation. The focus of this contribution is on disorder strengths below the reported values for the critical disorder $h_C$. \\ Our numerical results indicate that the isotropic Heisenberg chain in the absence of disorder exhibits super-diffusive dynamics governed by the KPZ universality class[1]. In particular, we confirm the value of the dynamical exponent $z=\frac{3}{2}$, reported previously[2], and show that the space-time dependence of the spin density correlator is consistent with KPZ scaling. Further evidence for KPZ behavior will be presented on the poster.\\ In the disordered chain, we generally observe slow dynamics far from diffusive behavior for $L\leq 32$ sites[3]. This slow dynamics manifests itself in the width of the propagator $\Delta x(t)$ as well as a non-gaussian spatial profile, which is typically close to an exponentially decaying shape. The dynamics appears subdiffusive in the sense that the time-dependent, effective exponent $\frac{d\ln(\Delta x(t))}{d\ln(t)} = \beta(t)$ is below the diffusive value $\beta(t) < 1/2$ in a large window of times, which is consistent with previous numerical studies (see [4] for a review). However, we find that $\Delta x(t)$ exhibits strong finite-size effects even if the single-particle localization length is of the order of the lattice constant. Most strikingly, for long enough chains, $\beta(t)$ exhibits a slow growth, which extends to longer times when the system size is increased further. While we cannot extract the asymptotic behavior from the numerical data, our results suggest that subdiffusion might be transient and eventually give way to conventional diffusion in the limit of long times and large system size.\\ Moreover, we show that slow dynamics is also present for strong disorder. Saturation of $\Delta x(t)$, implying localization of charge, is not observed on the time scales available, even for disorder strengths significantly exceeding $h_C$[5].\\ [1] F. Weiner, P. Schmitteckert, S. Bera and F. Evers, unpublished work [2] M. Ljubotina, M. Žnidarič and T. Prosen, Nature Communications vol. 8, 16117 (2017) [3] S. Bera, G. De Tomasi, F. Weiner and F. Evers, Phys. Rev. Lett. 118, 196801 (2017) [4] D. J. Luitz and Y. B. Lev, Ann. Phys. 1600350 (2017) [5] S. Bera, F. Weiner and F. Evers, unpublished work

### Local integrals of motion in the Anderson-Hubbard model with and without spin disorder

Wortis, Rachel

It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. While the states of any system can be expressed in terms of integrals of motion, the question of interest is whether these integrals of motion are local and if so on what length scale. The explicit identification of the optimally local pseudospins in specific systems is non-trivial. We consider the disordered Hubbard model and by studying a small system explore ways of identifying the most local choice of the integrals of motion with charge disorder alone and with both spin and charge disorder.

### Dephasing time in three-dimensional topological insulators with bulk disorder

Zhang, Yue

We study the mechanism of electron dephasing at the surface of three-dimensional topological insulator. With the bulk disorder, the electron on the surface will not only dephased by electron- electron interaction and electron-phonon interaction, but also goes through a random potential created by localized states in the bulk. We analyze the temperature dependence of the dephasing time caused by the localized states. Unlike traditional liner behavior in two dimension, the dephasing time of the surface states in three-dimensional topological insulators is more sensitive to temperature and has nontrivial power law depandance.

### Interaction-enhanced integer quantum Hall effect in disordered systems

Zheng, Junhui

We study transport properties and topological phase transition in two-dimensional interacting disordered systems. Within dynamical mean-field theory, we derive the Hall conductance, which is quantized and serves as a topological invariant for insulators, even when the energy gap is closed by localized states. In the spinful Harper-Hofstadter-Hatsugai model, in the trivial insulator regime, we find that the repulsive on-site interaction can assist weak disorder to induce the integer quantum Hall effect, while in the topologically non-trivial regime, it impedes Anderson localization. Generally, the interaction broadens the regime of the topological phase in the disordered system.