Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session Q35: Many-body Localization and Disordered Optical Lattices |
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Sponsoring Units: DAMOP Chair: David Weiss, Pennsylvania State University Room: 210B |
Wednesday, March 4, 2015 2:30PM - 2:42PM |
Q35.00001: Quantum computation using many-body localization Soonwon Choi, Sarang Gopalakrishnan, Norman Yao, Mikhail Lukin Conventional wisdom holds that a stable quantum bit --- the building block for a quantum computer --- requires an isolated degree of freedom. Here, we explore a new approach to quantum information processing using disordered, strongly interacting systems in the many-body localized (MBL) phase. Our approach makes use of a number of unique features of an MBL phase: a lack of thermalization, a locally gapped spectrum, and slow dephasing. We illustrate our main idea using a spin-1 model, demonstrating the ability to encode, decode and perform a universal set of gates. We extend this approach to generic MBL systems and discuss both limitations and possible experimental realizations. [Preview Abstract] |
Wednesday, March 4, 2015 2:42PM - 2:54PM |
Q35.00002: Dynamics of interacting quantum systems near the transition to a many-body localization phase E. Jonathan Torres-Herrera, Lea F. Santos Many-body localization (MBL) has become a very active field of research. The interest in the subject is motivated by indications of the existence of a MBL phase transition and by advances in experiments with optical lattices, which may serve as testbeds for corroborating theoretical predictions. A paradigmatic system that exhibits a MBL phase transition is the one-dimensional Heisenberg model with on-site disorder. Here, we study the dynamics of these systems. In particular, we report the observation of a power-law decay of the fidelity (survival probability) near the MBL transition. We provide numerical evidence suggesting that the exponent of this decay is related to the multifractal structure of the eigenstates through the so-called correlation dimension. [Preview Abstract] |
Wednesday, March 4, 2015 2:54PM - 3:06PM |
Q35.00003: Quantum quenches in the many-body localized phase Zlatko Papic, Maksym Serbyn, Dmitry Abanin Many-body localized (MBL) systems provide an example of ergodicity-breaking systems that cannot be described by conventional statistical mechanics. We show that the behaviour of local observables following a quantum quench is a direct probe of the MBL phase, which distinguishes it from both the Anderson insulator and the ergodic phase. For a global quench, we find that local observables reach stationary, highly non-thermal values at long times, which retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit a universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered here can be naturally implemented in systems of ultra cold atoms in disordered optical lattices, and the behaviour of local observables provides a direct experimental signature of many-body localization. [Preview Abstract] |
Wednesday, March 4, 2015 3:06PM - 3:18PM |
Q35.00004: A macroscopic ``order parameter'' for many-body localization Ronen Vosk, Mark Fischer, Ehud Altman, Michael Schreiber, Sean Hodgman, Henrik L\"uschn, Pranjal Bordia, Ulrich Schneider, Immanuel Bloch Recent theoretical progress in characterizing many-body localized systems has not been confronted so far with an experimental test. Here we present a theoretical analysis of new experimental results showing many-body localization of interacting fermions in a quasi periodic optical lattice potential. Specifically we consider the time evolution of a system prepared in a particular many-body initial state, a charge-density wave. Relaxation of the density-wave to a non-vanishing value at long times provides a direct demonstration of the breakdown of ergodicity in the many-body localized state and the saturation value can serve as an order parameter of this state. We investigate how this order parameter depends on the interaction strength and on the initial state. Moreover, we show how (temporal) fluctuations in this order parameter are connected to the entanglement-entropy growth, thus providing a distinguishing signature that could be observed in future experiments. Finally we propose new experiments that would demonstrate the persistence of local quantum coherence in this system. [Preview Abstract] |
Wednesday, March 4, 2015 3:18PM - 3:30PM |
Q35.00005: Many-body localization in the thermodynamic limit Deepak Iyer, Baoming Tang, Marcos Rigol We use thermalization indicators and numerical linked cluster expansions to probe the onset of many-body localization in a disordered one-dimensional hard-core boson model in the thermodynamic limit. We show that after equilibration following a quench, the momentum distribution indicates a freezing of one-particle correlations at higher values than if the system were in thermal equilibrium. The position of the delocalization to localization transition, identified by the breakdown of thermalization with increasing disorder strength, is found to be consistent with the value from the level statistics obtained via full exact diagonalization of finite chains. Our results strongly support the existence of a many-body localized phase in the thermodynamic limit. [Preview Abstract] |
Wednesday, March 4, 2015 3:30PM - 3:42PM |
Q35.00006: Thermalization at the Many-body localization Phase Transition Tarun Grover It has been recently found that sufficiently disordered, isolated quantum systems may fail to thermalize leading to a 'many-body localized' phase. In this phase the basic tenet of equilibrium statistical mechanics, namely, the equal likelihood for all microstates with the same energy, breaks down. A fundamental question is what happens as the disorder becomes weaker so that one approaches the localization-delocalization transition? In particular, does the system thermalize \textit{at} the transition? In this talk, I will show that certain general considerations involving the behavior of entanglement entropy close to the transition imply that at a continuous many-body localization transition, the system is fully thermalized in the sense that critical eigenstates show ergodic behavior. [Preview Abstract] |
Wednesday, March 4, 2015 3:42PM - 3:54PM |
Q35.00007: Many-body localization in periodically driven systems Dmitry Abanin, Pedro Ponte, Zlatko Papic, Francois Huveneers We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. MBL phase exhibits logarithmic in time growth of entanglement entropy for initial product states, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion (LIOM), which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggests a direct transition between the two phases. Our results show that many-body localization persists for sufficiently weak periodic driving, and that MBL-delocalization transition can be induced by sufficiently strong driving. [1] P. Ponte, Z. Papic, F. Huveneers, D. A. Abanin,arXiv:14108518 [2] P. Ponte et al., arXiv:1403.6480 [Preview Abstract] |
Wednesday, March 4, 2015 3:54PM - 4:06PM |
Q35.00008: Quantum quenches in a three-dimensional system exhibiting Anderson localization Smitha Vishveshwara, Armin Rahmani We theoretically study a quantum quench in fermionic lattice model that exhibits Anderson localization, in which a disorder potential is suddenly turned on in isolation from a thermal environment. We relate several physical observables of the system (including their temporal as well as sample-to sample fluctuations) to the statistical properties of the single-particle disordered wave functions and analyze their behavior as a function of disorder. In particular, we find a non-monotonic disorder dependence for sample-to-sample density fluctuations. We, furthermore, examine the equilibration of the system to generalized thermodynamic ensembles. We relate several of the observed features to the crossover from extended to localized behavior. [Preview Abstract] |
Wednesday, March 4, 2015 4:06PM - 4:18PM |
Q35.00009: Disorder effects on quantum quenches in cold-atom systems Christopher Hooley, Maximilian Schulz, Roderich Moessner We present a combined computational and theoretical study of the dynamics of cold gases of fermionic atoms after a sudden change of the Hamiltonian (a ``quantum quench''). In our proposed experiment, the pre-quench potential consists of an optical lattice, a harmonic trap, and uncorrelated site disorder (produced, for example, by exposing the atoms to laser speckle). The post-quench potential is the same, but with the centre of the harmonic trap shifted to one side. In the non-interacting case, we present results for the post-quench evolution of the density profile as the following parameters are varied: the pre-quench chemical potential; the disorder strength; and the distance over which the harmonic trap is displaced. We analyse these results in terms of the population of eigenstates of the post-quench Hamiltonian, as well as in terms of an effective model consisting of an open quantum system with a small number of degrees of freedom. Preliminary approaches to the inclusion of interatomic interaction effects are also discussed. [Preview Abstract] |
Wednesday, March 4, 2015 4:18PM - 4:30PM |
Q35.00010: Exact mobility edge in one dimensional quasiperiodic lattices Sriram Ganeshan We present localization properties of a family of nearest neighbor tight binding models with quasiperiodic onsite modulation. We prove that this family is self-dual under a generalized transformation. The self-dual condition for this general model turns out to be a closed form function of model parameters and energy. We numerically verify that this self-dual line is a mobility edge separating the localized and extended states. Our model is a first of its kind example of a nearest neighbor tight binding model with duality symmetry manifesting mobility edge. Our model provides analytical insight into the mobility edge physics of Anderson localization, a feature occurring in three or more dimensions. Quasiperiodic 1D lattices have been realized in ultracold atoms by a standing wave arrangement of two laser beam with mutually incommensurate wave vector. The quasiperiodic potentials we considered in this work can be systematically engineered by a controlled application of series of standing wave laser beams. We present a concrete schematic to realize our results in optical lattices and photonic waveguides. [Preview Abstract] |
Wednesday, March 4, 2015 4:30PM - 4:42PM |
Q35.00011: Phase diagram of bosons trapped in a two-dimensional quasi-periodic lattice Chao Zhang, Arghavan Safavi-Naini, Barbara Capogrosso-Sansone We report on results of Quantum Monte Carlo simulations for bosons in a two dimensional quasi-periodic optical lattice. We study the ground state phase diagram at unity filling and confirm the existence of three phases: superfluid, Mott insulator, and Bose glass. At lower interaction strength, we find that sizable disorder strength is needed in order to destroy superfluidity in favor of the Bose glass. On the other hand, at large enough interaction, superfluidity is completely destroyed in favor of the Mott insulator (at lower disorder strength) or the Bose glass (at larger disorder strength). At intermediate interactions, the system undergoes an insulator to superfluid transition upon increasing the disorder, while a further increase of disorder strength drives the superfluid to Bose glass phase transition. [Preview Abstract] |
Wednesday, March 4, 2015 4:42PM - 4:54PM |
Q35.00012: Superfluid - Insulator transition for bosons in disordered and quasi-periodic potentials Thierry Giamarchi, Chiara D'Errico, Eleonora Lucioni, Luca Tanzi, Lorenzo Gori, Guillaume Roux, Ian P. McCulloch, Massimo Inguscio, Giovanni Modugno On the theory side, one dimensional bosons in random [1] and quasiperiodic potentials [2] have been shown to undergo superfluid to insulator phase transitions, upon variation of the strength of the disorder or of the interactions. We discuss here such a transition in connection with the experiments in a system of $^39$K atoms for which both the disorder (quasiperiodic potential) and the interactions can be experimentally varied in a controlled way [3]. We analyze three probes of the nature of the system, namely a measurement of the coherence, the transport and the excitation spectrum obtained by shaking of the lattice. The combination of these measurements shows evidence of an insulating regime extending from weak to strong interaction and surrounding a superfluid-like regime, in general agreement with the theory. [1] T. Giamarchi and H. J. Schulz, Phys. Rev B {\bf 37} 325 (1988). [2] G. Roux, T. Barthel, I. P. McCulloch, C. Kollath, U. Schollw\"ock and T. Giamarchi, Phys. Rev. A {\bf 78} 023628 (2008). [3] Chiara D'Errico, Eleonora Lucioni, Luca Tanzi, Lorenzo Gori, Guillaume Roux, Ian P. McCulloch, Thierry Giamarchi, Massimo Inguscio and Giovanni Modugno Phys. Rev. Lett. {\bf 113}, 095301 (2014). [Preview Abstract] |
Wednesday, March 4, 2015 4:54PM - 5:06PM |
Q35.00013: Characterizing the Bose Glass Phase in Disordered Optical Lattices Eric Welch, Adam Chalupa, Byounghak Lee We present a theoretical study of disordered optical lattices using a mean-field approach to the Bose-Hubbard model. Through analyses on simple disorder configurations, such as binary and ternary random disorder potentials, we find that the phase transition at each lattice site is directly between Mott insulator and superfluid, contrary to the spatially averaged phase, where the transition between Mott insulator and superfluid is through the Bose glass phase. We also discuss the instability of the Bose glass phase in uniformly disordered systems in the terms of spatially averaged pure systems with chemical potential offsets. [Preview Abstract] |
Wednesday, March 4, 2015 5:06PM - 5:18PM |
Q35.00014: Searching for the Bose glass in disordered optical lattices with center-of-mass dynamics Mi Yan, Vito Scarola Ultracold atomic gases placed in optical lattices realize distinct many-body phases, including superfluids and Mott insulators. The addition of controlled disorder induces an additional phase, a Bose-Glass phase, that is difficult to unambiguously identify experimentally. We apply the time-dependent Gutzwiller mean-field method to model the transport properties of interacting bosons confined in disordered optical lattices after a sudden displacement of the underlying harmonic trapping potential. The edge superfluid is used to distinguish Bose glass and Mott insulator phases in the center of the trap by different center-of-mass dynamical signatures. We find that the edge superfluid oscillates after collision with the central Mott state. But the edge superfluid only drifts through a central Bose glass with a characteristic linear signature in long-time dynamics. Our work provides a method for experimental identification of the Bose glass in cold atom systems. [Preview Abstract] |
Wednesday, March 4, 2015 5:18PM - 5:30PM |
Q35.00015: Impurity-doped Bose-Einstein Condensates in Multi-mode Cavities Shahriar Shadkhoo, Robijn Bruinsma We study impurities in a Bose-Einstein Condensate (BEC), trapped in a multi-mode cavity which is transversely laser-pumped. The pure system has been proposed to exhibit emergent crystallinity for sufficiently strong pumping, and is therefore described by the quantum version of the fluctuation-induced first order phase transitions. We address the ground state of a quantum impurity coupled to the BEC, away from and near the phase transition. We show that this model system supports various perturbative and non-perturbative excitations around the particle. Light impurities form large and small polarons, whereas solitonic solutions may appear around heavier impurities. The effects of quantum and thermal fluctuations are also investigated. [Preview Abstract] |
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