Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session R25: Disorder and Localization in AMO Systems III: Many-body Localization |
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Sponsoring Units: DAMOP DCMP Chair: Fernando Sols, Complutense University Room: BCEC 160A |
Thursday, March 7, 2019 8:00AM - 8:12AM |
R25.00001: Long-range resonances and the meltdown of many-body localization Benjamin Villalonga, Bryan Clark Closed, quantum systems with interactions can transition to a many-body localized (MBL) phase in the presence of disorder. In this work, we attempt to numerically identify the presence of resonances in the ergodic-MBL transition. We find evidence for the proliferation of resonances around the transition, where the resonance structure becomes scale invariant. In addition, we consider how the resonances induce the buildup of entanglement and spectral statistics observed in the system through collisions between energy levels. We explore this both in the real-space basis as well as an adiabatic l-bit basis. |
Thursday, March 7, 2019 8:12AM - 8:24AM |
R25.00002: Critical Dynamics at the Many-Body-Localized Phase Transition Matthew Rispoli, Alexander Lukin, Robert Schittko, Sooshin Kim, Joyce Kwan, Ming E Tai, Julian Leonard, Markus Greiner When an isolated quantum system is prepared far from equilibrium, transport of its constituent particles allows it to relax by energy exchange throughout the remaining system. However, the addition of strong disorder in these interacting systems breaks down transport at a critical disorder strength as a consequence of many-body localization (MBL). Here, we study many-body localization in a 1-D system of interacting bosons with quasi-periodic disorder. Through the site-resolved, correlated density fluctuations, we extract a dynamic transport length and observe exceptionally slow transport near this critical disorder strength. We additionally verify the critical nature of the system's dynamics by tuning the total system size. Finally, we identify a microscopic mechanism of the interaction-driven delocalization via a sparse-resonant structure. This sparse structure persists into higher-order correlation functions and additionally identifies the many-body critical nature. These results and observed mechanism lay a foundation for characterizing dynamic many-body phases and studying other proposed microscopic mechanisms in interacting, disordered systems. |
Thursday, March 7, 2019 8:24AM - 8:36AM |
R25.00003: Avoiding Ergodicity: Localization in Clean Interacting Systems Yuval Baum, Evert van Nieuwenburg, Gil Refael Since the phenomenon of many-body-localization (MBL) was re-postulated more than a decade ago, it has attracted a great deal of attention. A key ingredient for achieving the MBL phase is disorder (randomness). The roots of this phase lie within the phenomenon of Anderson localization, where non-interacting particles form a localized non-ergodic phase. It is the question regarding the fate of Anderson localization in the presence of interactions that plants the seed |
Thursday, March 7, 2019 8:36AM - 8:48AM |
R25.00004: Dephasing Beyond the Markovian Limit; Implications for Many-Body Localization Seth Davis, Matthew Foster Despite progress in understanding many-body localization (MBL) in one-dimension, many questions remain with respect to the nature of the transition and the stability of the MBL phase. We envision approaching the MBL transition from the high-temperature ergodic phase. We search for signatures of the transition as a failure of dephasing, which prevents the infrared divergence of quantum conductance corrections in the ergodic phase in 1D and 2D. |
Thursday, March 7, 2019 8:48AM - 9:00AM |
R25.00005: Many Body Localization Transition in Systems with Correlated Disorder Rajdeep Sensarma, Abhisek Samanta, Ahana Chakraborty We study the transition from many body localized to ergodic transitions in disordered spin chains where the disorder at different sites are correlated. In the uncorrelated limit, the system has a well studied transition between many body localized to ergodic phase as a function of increasing disorder strength. On the other hand, in the extremely correlated limit, we essentially obtain a translation invariant system. We use two different models of correlated disorder and map out the phase diagram in the correlation-disorder plane. |
Thursday, March 7, 2019 9:00AM - 9:12AM |
R25.00006: Activating many-body localization in solids by driving Zala Lenarcic, Ehud Altman, Achim Rosch
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Thursday, March 7, 2019 9:12AM - 9:24AM |
R25.00007: Flow Equations for Many-Body Localisation: Dynamics and Dimensionality Steven Thomson, Marco Schiro Once thought to destroy localisation completely, we now know that adding interactions into disordered quantum matter can lead to the formation of a many-body localised phase. This phase is characterised by an extensive number of local conserved quantities and a failure to thermalise. Consequently it cannot be described by conventional equilibrium quantum statistical mechanics: new theoretical tools are required. Here, we present a semi-analytic flow equation approach that is capable of simulating large system sizes and of computing the real-time dynamics of observables and correlation functions. We employ a continuous unitary transform to diagonalise the Hamiltonian of a gas of interacting spinless fermions, show how local integrals of motion naturally emerge from this method, and go on calculate time evolution and localisation properties in the strongly-disordered regime in both one and two spatial dimensions. We further comment on ongoing work extending the method to incorporate additional features, including spin, as well as three-dimensional systems. |
Thursday, March 7, 2019 9:24AM - 9:36AM |
R25.00008: Localization in Fractonic Random Circuits Shriya Ramachandran Pai, Michael Pretko, Rahul Nandkishore In this talk, I will describe a new mechanism for many-body localization, making use of ideas drawn from the field of fractons. Specifically, I will present results on the spreading of initially local operators under random unitary evolution in spin chains subject to fracton conservation laws, such as conservation of dipole moment. We find that fractons remain permanently localized at their initial positions, providing a crisp example of a non-ergodic dynamical phase of random unitary evolution. These results can be interpreted as a consequence of the properties of low-dimensional random walks. This mechanism for localization remains robust in one and two dimensions, but breaks down in three-dimensional fracton systems. We argue that these results extend to Floquet and Hamiltonian time evolution, even in the absence of disorder, thereby providing a mechanism for many-body localization in a translationally invariant system. |
Thursday, March 7, 2019 9:36AM - 9:48AM |
R25.00009: Statistics of entanglement spectrum across MBL to ergodic transition. Abhisek Samanta, Kedar Damle, Rajdeep Sensarma We show how the statistics of entanglement spectra change across the transition between a many body localized phase and an ergodic phase of an interacting disordered system. Using a disordered spin chain as a model, we numerically construct various measures and try to find an "order parameter" for the transition. The transition point obtained from this construction matches with those obtained from other indicators like the distribution of many-body energy gaps. |
Thursday, March 7, 2019 9:48AM - 10:00AM |
R25.00010: Localization in an interacting system with two degrees of freedom per site: Is charge disorder alone sufficient to localize the Hubbard model or is spin disorder also necessary? Rachel Wortis, Brandon Leipner-Johns Many-body localization, the inability of some isolated quantum systems with both interactions and disorder to achieve thermal equilibrium, has been studied primarily in systems with one degree of freedom per site. The addition of a second degree of freedom creates a new avenue for exploration and connects to the Hubbard model, a launch point for the study of a wide range of systems of current interest including transition metal oxides and cold atoms in optical lattices. With both charge and spin degrees of freedom at each site, is disorder in just one of these channels sufficient to cause the full system to be localized? Alternatively, does the degree of freedom without disorder delocalize the one which sees disorder? To what extent is the level of localization in one channel related to the disorder in the other channel? We consider the Hubbard model with both charge and spin disorder. We employ several measures of localization designed to treat spin and charge on equal footing. We find measures based on the local integrals of motion are consistent with those based on the dynamics. For sufficient disorder in one degree of freedom, only a small amount of disorder in the other degree of freedom localizes both degrees of freedom. |
Thursday, March 7, 2019 10:00AM - 10:12AM |
R25.00011: Many-body localization in a multifractal fermionic chain Nicolas Macé, Nicolas Laflorencie, Fabien Alet We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a deterministic quasiperiodic on-site potential following the Fibonacci sequence. With this choice, the single-particle eigenstates are delocalized and multifractal, no matter how strong the potential is. |
Thursday, March 7, 2019 10:12AM - 10:24AM |
R25.00012: Many body localization in the presence of a central qudit Nathan Ng, Michael Kolodrubetz We consider a many-body localized system coupled globally to a central d-level system. Under an appropriate scaling of d and system size, we find evidence that the localized phase survives. We argue for two possible thermalizing phases, depending on whether the qudit becomes fully ergodic. This system provides one of the first examples of many-body localization in the presence of long-range (non-confining) interactions. We discuss possible anomalous behavior in the system, such as an inverted mobility edge - localized at high temperature, but ergodic at low temperature. |
Thursday, March 7, 2019 10:24AM - 10:36AM |
R25.00013: Stability of quasiperiodic chains to quantum avalanches Anushya Chandran, Philip Crowley In one dimension, it is conjectured that full many-body localization is unstable if the localization length exceeds a threshold value. The instability is due to the presence of rare ergodic Griffiths regions; each such region thermalizes its environment and grows, resulting in a (slow) avalanching process of thermalization. We show that weakly interacting chains with quasiperiodic potentials violate this conjecture because the sparse local structure of the l-bits prevents thermalization near an ergodic region. Our work identifies the first qualitative difference between random and quasi-periodic localization and suggests new experimental tests of avalanche instabilities. |
Thursday, March 7, 2019 10:36AM - 10:48AM |
R25.00014: Hilbert space properties of the many-body localization problem: from full ergodicity to multifractality Nicolas Macé, Fabien Alet, Nicolas Laflorencie In contrast with Anderson localization where a genuine localization is observed in real space, the many-body localization (MBL) problem is much less understood in the Hilbert space, support of the eigenstates. In this work, using exact diagonalization techniques up to L=24 spin-1/2 particles (i.e. Hilbert space of size N=2.7 millions) we address the ergodicity properties in the underlying N-dimensional complex networks spanned by various computational bases. We report fully ergodic eigenstates in the delocalized phase (irrespective of the computational basis), while the MBL regime features a generically (basis-dependent) multifractal behavior, delocalized but non-ergodic. The MBL transition is signaled by a non-universal jump of the multifractal dimensions. |
Thursday, March 7, 2019 10:48AM - 11:00AM |
R25.00015: Entanglement, dynamics and breakdown of many-body localization in current driven system Sumilan Banerjee, Animesh Panda What is the fate of a many-body localized system under a voltage bias between two ends? Can the system undergo a transition to a current carrying non-equilibrium steady state and how the entanglement properties of the quantum states change across the transition? Motivated by these questions, we model a current driven interacting disorder system through a non-Hermitian Hamiltonian and study the entanglement properties of its eigenstates. We also discuss the dynamics, entanglement growth and long-time fate of a generic initial state under an appropriate time-evolution of the system governed by the non-Hermitian Hamiltonian. Our study reveals rich entanglement structures of current driven states and multiple dynamical transitions as a function of disorder and the strength of the non-Hermitian term, that is related to the external bias. |
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