Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session H50: Many-Body Localization in Atomic Systems II |
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Sponsoring Units: DAMOP Room: Hilton Baltimore Holiday Ballroom 1 |
Tuesday, March 15, 2016 2:30PM - 2:42PM |
H50.00001: Characterizing eigenstate thermalization via measures in the Fock space of operators Xiao-Liang Qi, Pavan Hosur The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in various regimes, by mapping general interacting quantum systems on regular lattices onto a single particle living on a high-dimensional graph. By numerically analyzing deviations from ETH behavior in the non-integrable Ising model, we propose quantities that we call the "n-weight" and the "n-distinguishability" to democratically characterize the average and the maximum deviations, respectively, for all operators residing on n sites. Along the way, we discover that complicated operators on average are worse than simple ones at distinguishing between neighboring eigenstates, contrary to the naive intuition created by the usual statements of the ETH that few-body (many-body) operators acquire the same (different) expectation values in nearby eigenstates at finite energy density. [Preview Abstract] |
Tuesday, March 15, 2016 2:42PM - 2:54PM |
H50.00002: Dynamical Many-Body Localization in a System of Coupled Relativistic Kicked Rotors Efim Rozenbaum, Victor Galitski A periodically-driven rotor is a prototypical model that exhibits a transition to chaos in the classical regime and dynamical localization (related to Anderson localization) in the quantum regime. In a recent preprint, {\tt arXiv:1506.05455}, Keser {\it et al.} considered a many-body generalization of coupled quantum kicked rotors, and showed that in the special integrable linear case, the dynamical localization survives interactions. By analogy with many-body localization, the phenomenon was dubbed dynamical many-body localization (DMBL). In the present work, we study a non-integrable model of coupled quantum relativistic kicked rotors. Our analysis of such coupled ``kicked'' Dirac equations indicates that DMBL can exist for generic, non-integrable systems. We also analyze quantum dynamics of the model, which for certain select values of model's parameters exhibits highly unusual behavior -- e.g., superballistic transport and peculiar spin dynamics. [Preview Abstract] |
Tuesday, March 15, 2016 2:54PM - 3:06PM |
H50.00003: A renormalization group approach to identifying the local quantum numbers in a many-body localized system David Pekker, Bryan K. Clark, Vadim Oganesyan, Gil Refael, Binbin Tian Many-body localization is a dynamical phase of matter that is characterized by the absence of thermalization. One of the key characteristics of many-body localized systems is the emergence of a large (possibly maximal) number of local integrals of motion (local quantum numbers) and corresponding conserved quantities. We formulate a robust algorithm for identifying these conserved quantities, based on Wegner’s flow equations – a form of the renormalization group that works by disentangling the degrees of freedom of the system as opposed to integrating them out. We test our algorithm by explicit numerical comparison with more engineering based algorithms – Jacobi rotations and bi-partite matching. We find that the Wegner flow algorithm indeed produces the more local conserved quantities and is therefore more optimal. A preliminary analysis of the conserved quantities produced by the Wegner flow algorithm reveals the existence of at least two different localization lengthscales. [Preview Abstract] |
Tuesday, March 15, 2016 3:06PM - 3:18PM |
H50.00004: Many-body localization and thermalization in disordered Hubbard chains Rubem Mondaini, Marcos Rigol Recently, a lot of attention has been given to the aspects that lead isolated interacting quantum systems to thermalize. In the presence of disorder, however, the thermalization process fails resulting in a phenomena where transport is suppressed known as many-body localization. Unlike the standard Anderson localization for non-interacting systems, the delocalized (ergodic) phase is very robust against disorder even for moderate values of interaction. Another interesting aspect of the many-body localization phase is that under the time evolution of the quenched disorder, information present in the initial state may survive for arbitrarily long times. This was recently used as a probe of many-body localization of ultracold fermions in optical lattices with quasi-periodic disorder\footnote{M. Schreiber \textit{et al.}, Science, \textbf{349} 842 (2015)}. Here, we will use numerical results in one-dimensional Hubbard chains to show that this analysis may suffer from substantial finite-size effects. We will also compare different types of disorder to see how the ergodicity is affected.\footnote{R. Mondaini and M. Rigol, Phy. Rev. A \textbf{92}, 041601(R) (2015)} [Preview Abstract] |
Tuesday, March 15, 2016 3:18PM - 3:30PM |
H50.00005: Particle-hole symmetry, many-body localization, and topological edge modes Romain Vasseur, Aaron J. Friedman, S.A. Parameswaran, Andrew C. Potter We study the excited states of interacting fermions in one dimension with particle-hole symmetric disorder (equivalently, random-bond XXZ chains) using a combination of renormalization group methods and exact diagonalization. Absent interactions, the entire many-body spectrum exhibits infinite-randomness quantum critical behavior with highly degenerate excited states. We show that though interactions are an irrelevant perturbation in the ground state, they drastically affect the structure of excited states: even arbitrarily weak interactions split the degeneracies in favor of thermalization (weak disorder) or spontaneously broken particle-hole symmetry, driving the system into a many-body localized spin glass phase (strong disorder). In both cases, the quantum critical properties of the non-interacting model are destroyed, either by thermal decoherence or spontaneous symmetry breaking. This system then has the interesting and counterintuitive property that edges of the many-body spectrum are \emph{less} localized than the center of the spectrum. We argue that our results rule out the existence of certain excited state symmetry-protected topological orders. [Preview Abstract] |
Tuesday, March 15, 2016 3:30PM - 3:42PM |
H50.00006: Dynamical many-body localization in an integrable model Ayin C. Keser, Sriram Ganeshan, Gil Refael, Victor Galitski We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifest both localization and delocalization in momentum space. We explicitly show that, for this model, the energy being bounded at long times is neither a necessary nor a sufficient condition for dynamical localization. We present a set of integrals of motion, which can serve as a fundamental diagnostic of dynamical localization. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models. [Preview Abstract] |
Tuesday, March 15, 2016 3:42PM - 3:54PM |
H50.00007: Dynamics of Hubbard-Band Quasiparticles in Disordered Optical Lattices Vito Scarola, Brian DeMarco Recent experiments use transport of degenerate Fermi gases in optical lattices (Kondov et al. Phys. Rev. Lett. 114, 083002 (2015)) to probe the interplay of disorder and strong interactions. These experiments find evidence for an intriguing insulating phase where quantum diffusion is completely suppressed by strong disorder. Quantitative interpretation of these experiments remains an open problem that requires inclusion of non-zero entropy, strong interaction, and trapping in an Anderson-Hubbard model. We construct a theory of dynamics of Hubbard-band quasiparticles tailored to trapped optical lattice experiments. We compare the theory directly with center-of-mass transport experiments of Kondov et al. with no fitting parameters. The close agreement between theory and experiments shows that the suppression of transport is only partly due to finite entropy effects. We argue that the complete suppression of transport is consistent with short-time, finite size precursors of Anderson localization of Hubbard-band quasiparticles. The combination of our theoretical framework and optical lattice experiments offers an important platform for studying localization in isolated many-body quantum systems. [Preview Abstract] |
Tuesday, March 15, 2016 3:54PM - 4:06PM |
H50.00008: Many-body localization and symmetry protected topology with ultracold Rydberg atoms Ionut-Dragos Potirniche, Monika Schleier-Smith, Ashvin Vishwanath, Norman Yao The interplay between quantum entanglement and symmetry-protected topological order has led to the classification of gapped, interacting, one dimensional quantum phases. A consequence of this classification is the existence of a diverse set of exactly solvable models, which serve as paradigmatic examples of various SPT orders. The experimental realization of such models has been hampered by the challenge of implementing tunable multi-body interactions. Recently, an alternate strategy has arisen: periodic driving. Indeed, it has been shown that the dynamics of a simple Floquet transverse-field Ising model can mirror that of the celebrated Haldane chain. However, as SPT order is expected only in the ground state while a driven system is expected to heat to infinite temperature, the ability to observe such “Floquet” SPT phases remains an open question. Here, we demonstrate that strong disorder, leading to many-body localization, stabilizes SPT order at finite energy densities while also preventing arbitrary heating of the system. Moreover, we propose a natural experimental implementation in a 1D optical lattice of ultracold Rydberg atoms. [Preview Abstract] |
Tuesday, March 15, 2016 4:06PM - 4:18PM |
H50.00009: Probing Anderson localization of light via decay rate statistics in aperiodic Vogel spirals Aristi Christofi, Felipe A. Pinheiro, Luca Dal Negro We systematically investigate the spectral properties of different types of two-dimensional aperiodic Vogel spiral arrays of pointlike scatterers and three-dimensional metamaterials with Vogel spiral chirality using rigorous Green’s function spectral method. We considered an efficient T-matrix approach to analyze multiple-scattering effects, including all scattering orders, and to understand localization properties through the statistics of the Green’s matrix eigenvalues. The knowledge of the spectrum of the Green matrix of multi-particle scattering systems provides important information on the character of light propagation and localization in chiral media with deterministic aperiodic geometry. In particular, we analyze for the first time the statistics of the eigenvalues and eigenvectors of the Green matrix and extract the decay rates of the eigenmodes, their inverse participation ratio (IPR), the Wigner delay times and their quality factors. We emphasize the unique properties of aperiodic Vogel spirals with respect to random scattering media, which have been investigated so far. [Preview Abstract] |
Tuesday, March 15, 2016 4:18PM - 4:30PM |
H50.00010: Anomalous transport in ergodic lattice systems Yevgeny Bar Lev, David R. Reichman Many-body localization transition is a peculiar dynamical transition between ergodic and non-ergodic phases, which may occur at any temperature and in any dimension. For temperatures below the transition the system is nonergodic and localized, such that conductivity strictly vanishes at the thermodynamic limit, while for temperatures above the transition the system is thermal and conductive. In this talk I will present a comprehensive study of the dynamical properties of the ergodic phase in one and two dimensional generic disordered and interacting systems, conducted using a combination of nonequilibrium diagrammatic techniques and numerically exact methods. I will show that the ergodic phase, which was expected to be diffusive, exhibits anomalous transport regime for nontrivial times and explain how our findings settle with phenomenological theoretical models. [Preview Abstract] |
Tuesday, March 15, 2016 4:30PM - 4:42PM |
H50.00011: Eigenstate Order in Floquet Systems Curt Von Keyserlingk, Shivaji Sondhi Recent work has introduced the notion of eigenstate order for many body systems and extended it to periodically driven, or Floquet, systems. I will discuss a set of results on possible phases in Floquet systems. These involve generalisations of topological insulators and superconductors as well as generalisations of interacting symmetry protected and topological phases of matter. Many body localisation plays an essential role in their realisation. [Preview Abstract] |
Tuesday, March 15, 2016 4:42PM - 4:54PM |
H50.00012: Localization in systems with long-range interactions Lea Santos, Francisco Perez-Bernal, Fausto Brogonovi, Giuseppe Celardo In recent experiments with ion traps, long-range interactions were associated with the very fast propagation of excitations. Here, we show that, depending on the initial state, the evolution of these systems may actually be exceedingly slow. This is justified with the analysis of the density of states and structures of the eigenstates, and confirmed with numerical simulations of quench dynamics. The two sources of restricted dynamics that we discuss are: the presence of an excited state quantum phase transition and the onset of subspaces shielded from the effects of long-range interactions. Both scenarios can be tested experimentally. [Preview Abstract] |
Tuesday, March 15, 2016 4:54PM - 5:06PM |
H50.00013: Dynamics of a Many-Body-Localized System Coupled to a Bath Mark Fischer, Mykola Maksymenko, Ehud Altman Coupling a many-body localized system to a dissipative bath necessarily leads to delocalization. Here we investigate the nature of the ensuing relaxation dynamics and the information it holds on the many-body localized state. To solve for the time evolution, we formulate the relevant Lindblad equation in terms of the local integrals of motion of the underlying localized Hamiltonian. This allows to map the quantum evolution deep in the localized state to tractable classical rate equations. We consider two different types of dissipation relevant to systems of ultra-cold atoms: particle loss and dephasing due to inelastic scattering on the lattice lasers. Only the first mechanism shows a pronounced effect of interactions on the relaxation of observables. [Preview Abstract] |
Tuesday, March 15, 2016 5:06PM - 5:18PM |
H50.00014: Extended slow dynamical regime near the many-body localization transition David J. Luitz, Nicolas Laflorencie, Fabien Alet Many-body localization is characterized by a slow logarithmic growth of entanglement entropy after a global quantum quench while the local memory of an initial spin imbalance remains at infinite time. We address the dynamics in the delocalized ergodic regime, where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibium dynamics of the random-field Heisenberg chain is studied up to L = 28 sites, starting from an initially unantangled high-energy product state. With such a global quench protocol, we study the time evolution of the entanglement entropy, as well as the spin density imbalance in order to make contact with recent cold atom experiments. Within most of the delocalized phase, we unambiguously find a sub-ballistic entanglement growth $S(t) \propto t^{1/z}$ with a disorder-dependent exponent $z \geq 1$, in contrast with the pure ballistic growth $z = 1$ of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $I(t) \propto t^{-\zeta}$ with a continuously varying disorder- dependent exponent $\zeta$, vanishing at the transition. This provides a clear experimental signature for detecting this non-conventional metallic state where transport is sub-diffusive. [Preview Abstract] |
Tuesday, March 15, 2016 5:18PM - 5:30PM |
H50.00015: Effective localization potential of quantum states in disordered media Filoche Marcel, Douglas N. Arnold, Guy David, David Jerison, Svitlana Mayboroda The amplitude of localized quantum states in random or disordered media may exhibit long range exponential decay. We present here a theory that unveils the existence of a localization landscape that controls the amplitude of the eigenstates in any quantum system. For second order operators such as the Schrödinger operator, this localization landscape is simply the solution of a Dirichlet problem with uniform right-hand side [1]. Moreover, we show that the reciprocal of this landscape plays the role of an effective potential which finely governs the confinement of the quantum states. In this picture, the boundaries of the localization subregions for low energy eigenfunctions correspond to the barriers of this effective potential, and the long range exponential decay characteristic of Anderson localization is explained as the consequence of multiple tunneling in the dense network of barriers created by this effective potential. Finally, we show that the Weyl's formula based on this potential turns out to be a remarkable approximation of the density of states for a large variety of systems, periodic or random, 1D, 2D, or 3D. [1] M. Filoche and S. Mayboroda, Proceedings of the National Academy of Sciences of the USA 109, 14761 (2012). [Preview Abstract] |
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