Session B01: Disorder and Localization in AMO Systems

Many-body delocalization of ultracold bosons in lattices

Many-body localization describes the phenomenon of localization and vanishing charge transport in closed quantum many-body systems. It is well accepted by now that MBL is stable in one dimension and many of its properties have been revealed. Much less is known in two dimensions. Here we present our recent results on the study of the stability of the localization in 2d bosonic lattice systems. Our observation is consistent with persistent localization if the system is brought in contact with a small quantum bath, but localization is clearly destroyed for larger baths. The dynamics towards the steady state differs strongly in the two cases.   

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain

We study spin transport in a Hubbard chain with a strong, random, on-site potential and with spin-dependent hopping integrals t_σ. For the SU(2) symmetric case t_↑ = t_↓, such a model exhibits only partial many-body localization with localized charge and (delocalized) subdiffusive spin excitations [1,2]. In our work [3], we demonstrate that breaking the SU(2) symmetry by even weak spin asymmetry, t_↑ ≠ t_↓, localizes spins and restores full many-body localization. To this end, we derive an effective spin model where the spin subdiffusion is shown to be destroyed by arbitrarily weak t_↑ ≠ t_↓. Instability of the spin subdiffusion originates from an interplay between random effective fields and singularly distributed random exchange interactions.

[1] P. Prelovsek, O. S. Barisic, and M. Znidaric, Phys. Rev. B 94, 241104(R) (2016).
[2] M. Kozarzewski, P. Prelovsek, and M. Mierzejewski, Phys. Rev. Lett. 120, 246602 (2018).
[3] M. Sroda, P. Prelovsek, and M. Mierzejewski, Phys. Rev. B 99, 121110(R) (2019).   

Many-body localization from a one-particle perspective in the disordered 1D Bose-Hubbard model

We numerically investigate 1D Bose-Hubbard chains with onsite disorder by means of exact diagonalization. Consistent with previous studies, we observe signatures of transition from the ergodic to the many-body localized (MBL) regime when increasing the disorder strength or energy density. Apart form the entanglement entropy as a conventional but indirect measure for the ergodic-MBL transition we utilise the one-particle density matrix (OPDM) to characterize the system [1]. We show that the natural orbitals (the eigenstates of OPDM) are extended in the ergodic phase and real-space localized when one enters into the MBL phase. Furthermore, the distributions of occupancies of the natural orbitals as well as the diagonal part of OPDM (i.e., the site occupancies) can be used as measures of Fock-space localization in the respective basis [2]. Moreover, the full distribution of the densities of the physical particles provides a one-particle measure for the detection of the ergodic-MBL transition which could be directly accessed in experiments with ultra-cold gases.

[1] S. Bera, H. Schomerus, F. Heidrich-Meisner and J.H. Bardarson, PRL 115, 046603 (2015).
[2] M. Hopjan and F. Heidrich-Meisner, in preparation.   

Localization dynamics in a centrally coupled system

We investigate a disordered Ising chain in which all spins couple to a central qudit, through which spin flip interactions are mediated. For small but finite coupling, the trivial localization of the non-coupled limit survives as a form of many-body localization (MBL). By using an exact wavefunction propagation method, we are able to observe the dynamics of large system sizes (L~50-100) to intermediate timescales and establish the existence of slow or vanishing relaxation. This allows us to address the question of the proper scaling of the qudit size with L in the thermodynamic limit, the suppression of effective all-to-all coupling to protect MBL, and the dependence of localization on energy density.   

Strongly resonating clusters around the ergodic-MBL transition

An interacting quantum system can transition from an ergodic to a many body localized (MBL) phase under the presence of sufficiently large disorder. Both phases are radically different in their dynamical properties, which are characterized by highly excited energy eigenstates. One of the differences between both phases is in the statistics of their energy levels: while in an ergodic phase levels experience repulsion and follow GOE statistics, in MBL they largely lack repulsion and follow Poisson statistics. Here, we argue that the transition between both behaviors is accompanied by the formation of resonating clusters in the eigenstates of the Hamiltonian. Using a basis of local integrals of motion (l-bits), we observe that these clusters take the form of cat states over a subset of l-bits on a 1D spin chain. While such resonances are rare in MBL, they proliferate around the transition, and are absent well into the ergodic phase. Finally, the spatial structure of the resonating clusters suggests correlations that are scale invariant in the chain, which we check numerically for finite size systems.   

Inverted many-body mobility edge in a central qudit problem

We study the disordered Ising model with transverse and longitudinal fields coupled globally to a d-level system (qudit). In the center of the many-body spectrum, earlier work [PRL 122, 240402 (2019)] found a regime where many-body localization (MBL) survives global coupling to the cavity. In this work, we study the dependence of MBL on energy. Most strikingly, we discover an inverted mobility edge, where high energy states are localized while low energy states are delocalized. Our results are supported by shift-and-invert eigenstate targeting and Krylov time evolution up to L=13 and 18 respectively, with large central spin d=12 that is effectively infinite. We argue for critical energy of the MBL to thermal phase transition which scales as E_c∝L^½, consistent with finite size numerics. We also show evidence for a reentrant MBL phase at even lower energies despite the presence of strong effects of the central qudit in this regime.   

Emergent ergodicity at the transition between many-body localized phases

Due to their failure to thermalize, systems in the many-body localized (MBL) phase can support non-trivial order ( e.g. order characterized by spontaneously broken symmetries or symmetry-protected topological order) even in highly excited, many-body eigenstates. However, the stability of MBL as a system transitions between different ordered phases remains a mystery. In particular, it is unknown whether the competition between two orders near a phase boundary inevitably destabilizes the MBL and restores ergodicity to the system. Here, we present evidence that, indeed, a direct transition between different MBL phases cannot occur, and between any two MBL phases, an intervening finite-width thermalizing phase emerges. We probe the emergence of this thermalizing phase by numerically studying the level statistics of a variety of different models exhibiting either symmetry broken order or symmetry-protected topological order, both in the static and driven case. We complement our numerical analysis by providing an analytic picture for the instability of MBL around the phase transition.   

Critical properties of the many-body Aubry-Andre model localization-delocalization transition.

As opposed to random disorder, which localizes single-particle wave-functions in 1D at arbitrarily small disorder strengths, there is a localization-delocalization transition for quasi-periodic disorder in the 1D Aubry-Andre model at a finite disorder strength. On the single-particle level, many properties of the ground-state critical behavior have been revealed by applying a real-space renormalization-group scheme; the critical properties are determined solely by the continued fraction expansion of the incommensurate frequency of the disorder. We investigate the many-particle localization-delocalization transition in the Aubry-Andre model with and without interactions. In contrast to the single-particle case, we find that the critical exponents depend on a Diophantine equation relating the incommensurate frequency of the disorder and the filling fraction which generalizes the dependence, in the single-particle spectrum, on the continued fraction expansion of the incommensurate frequency. Numerical evidence suggests that interactions may be irrelevant at at least some of these critical points, meaning that the critical exponent relations obtained from the Diophantine equation may actually survive in the interacting case.   

Single doublons as ergodic bubbles

We illustrate a remarkably simple mechanism in which single doublon excitations trigger the generation of ergodic bubbles, which thermalize extensive localized systems. We provide analytical estimates showing how the critical disorder strength for such mechanism depends on singlon densities, which are nicely supported by numerical exact-diagonalization simulations. Our predictions equally apply to fermionic and bosonic systems and are definitively accessible by ongoing experiments simulating synthetic quantum lattices.   

Quasi-1D limit of the integer quantum Hall transition as a disordered Thouless pump

We study the quantum Hall plateau transition on rectangular tori. As the torus aspect ratio is increased, the 2D critical behavior (where a subextensive number of topological states exist in a vanishing energy window around a critical energy) changes drastically. In the thin-torus limit, the entire spectrum is Anderson-localized; however, an extensive number of states retain a nonzero Chern number. This apparent paradox is resolved by mapping the thin-torus quantum Hall system onto a disordered Thouless pump. We show that the Chern number maps onto the winding number of an electron’s path in real space during a pump cycle, and that the electrons' paths become random walks of diverging length, giving rise to the proliferation of large and essentially random Chern numbers across the spectrum. Building on this thin-torus limit result, we characterize quantitatively the crossover between the 1D and 2D regimes for large but finite aspect ratio. Possible realizations of this physics in quantum simulation platforms (e.g. cold atoms, microwave cavity arrays) are discussed.

Reference: M. Ippoliti and R. N. Bhatt, preprint at arXiv:1905.13171.   

Spin transport in disordered long-range interacting spin chain

We numerically study spin transport and spin-density profiles after a local quench in a disordered one-dimensional spin-chain with long-range interactions, in the regime where delocalization is predicted by all existing theories. We observe a transient super-diffusive transport, followed by asymptotic diffusive behavior. We provide a phenomenological explanation by properly generalized Griffiths picture.   

Complex network description of phase transitions in the classical and quantum disordered Ising Model

Complex network analysis is a powerful tool to describe and characterize classical systems such as the Ising model in a transverse magnetic field. Measuring spin-spin correlations gives rise to the adjacency matrix, representing a weighted network. In this study, the spin-spin correlations at different temperatures are analytically calculated, yielding phase-dependent complex networks, from simple networks in the low temperature ferromagnetic limit to random ones at high temperature. The network structure varies as the transverse field and temperature change, recovering the phase diagram and providing initial insight into correlations in the critical region. Analyzing the resulting complex network using a variety of network measures such as the degree histogram, average clustering, betweenness centrality and the graph entropy, the complexity is characterized. This method is applied for both the disordered classical Ising and quantum Ising lattice, demonstrating the role of finite temperature and disorder in generation of complexity.   

Probing Slow Scrambling in MBL and the Random Singlet Phase

We characterize the spreading of operators and entanglement in two paradigmatic non-thermalizing phases - the many body localized phase and the random singlet phase - using out-of-time-ordered correlators, the entanglement contour, and operator entanglement. We contrast these phases with strongly thermalizing holographic conformal field theories and fully localized Anderson insulators. We obtain a phenomenological description of the operator and state dynamics of these phases and provide credence to the utility of the entanglement contour and operator entanglement measures as useful probes of slowly scrambling and non-thermalizing dynamics.