Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session X27: Disorder and Localization in AMO Systems IFocus

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Sponsoring Units: DAMOP DCMP Chair: Vito Scarola, Virginia Tech Room: LACC 404B 
Friday, March 9, 2018 8:00AM  8:36AM 
X27.00001: Measuring Localization from Disorder and Strong Interactions: Ultracold Atoms in Optical Lattices Invited Speaker: Brian DeMarco

Friday, March 9, 2018 8:36AM  8:48AM 
X27.00002: Characterization of Classical and Quantum Chaos With OutofTimeOrdered Correlator in Stadium Billiard Efim Rozenbaum, Sriram Ganeshan, Victor Galitski Outoftimeordered correlator (OTOC) has been gaining attention as an indicator of chaos in quantum systems due to its simple interpretation in semiclassical limit. In particular, its rate of exponential growth at $\hbar_{\rm eff} \to 0$ is closely related to the classical Lyapunov exponent. The Bunimovich stadium billiard is a seminal classically chaotic model in which a particle moves freely inside a twodimensional stadiumshaped infinite potential well. We analyze this system and find that suitably defined OTOC in appropriate parameter regimes shows earlytime exponential growth (up to the Ehrenfesttime scale) at a rate attributed to the Lyapunov exponent. We also show that the WignerDyson level statistics related to the chaotic nature of the classical billiard can be extracted from the latetimeOTOC matrix. These findings make OTOC a unified tool for characterization of classical and quantum chaos. 
Friday, March 9, 2018 8:48AM  9:00AM 
X27.00003: Fidelity Plateaux from Correlated Noise in ColdAtom Quantum Simulators Christopher Hooley, Scott Taylor We demonstrate that, in a quantum simulation protocol based on the Hubbard model, correlated noise in the Hubbard parameters leads to arbitrarily long plateaux in the statepreparation fidelity as a function of elapsed time. We argue that this correlatednoise scenario is the generic one in the coldatom context, since all of the Hubbardmodel parameters ultimately depend on the same set of lasers. We explain the formation of such a plateau using the Blochsphere representation, deriving analytical expressions for its start and end times and its height. 
Friday, March 9, 2018 9:00AM  9:12AM 
X27.00004: NonPowerLaw Universality in OneDimensional Quasicrystals Attila Szabó, Ulrich Schneider In this talk I will present a study of the scaling properties of the Aubry–André model and related onedimensional quasiperiodic models near their localisation transitions. We find numerically that the scaling of energies near the ground state, usually captured by a single dynamical exponent, does not obey a power law relation. Instead, the scaling behaviour depends strongly on the correlation length in a manner governed by the continued fraction expansion of the irrational number β describing incommensurability in the system. In particular, arbitrarily close values of β can result in qualitatively different behaviours very close to the localisation transition. We find that this behaviour is universal between a range of models and can, for the Aubry–André model, be understood in terms of a discrete renormalisation group protocol. 
Friday, March 9, 2018 9:12AM  9:24AM 
X27.00005: Entanglement phase transitions from holographic random tensor networks Romain Vasseur, Andrew Potter, Yi Zhuang You, Andreas Ludwig In this talk, I will discuss new types of quantum phase transitions between arealaw and volumelaw entangled states. An example of such an entanglement phase transition is provided by the manybody localization transition in disordered quantum systems that separates a thermalizing phase at weak disorder from a manybody localized phase at strong disorder where statistical mechanics breaks down. In the spirit of random matrix theory, I will describe a simple model for such transitions where a physical quantum spin system lives at the (“holographic”) boundary of a bulk random tensor network. By mapping the calculation of the entanglement properties of the boundary system onto a classical statistical mechanics model, I will argue that one can get an analytic handle on the field theory of these entanglement transitions. 
Friday, March 9, 2018 9:24AM  9:36AM 
X27.00006: Logarithmic entanglement growth and its fragility in systems of trapped spinless fermions Maximilian Schulz, Christopher Hooley, Roderich Moessner, Frank Pollmann We consider a system of spinless fermions in a strong optical lattice plus a harmonic trap and 
Friday, March 9, 2018 9:36AM  9:48AM 
X27.00007: Approaching the ManyBody Localization Transition using Matrix Product States: Absence of GriffithsType Dynamics in a Thermalizing Quasiperiodic System Benjamin Dickens, Ehud Altman, Frank Pollmann During the last decade, a vast body of theoretical work has emerged to characterize the manybody localization (MBL) transition induced by quenched random disorder in 1D lattice models. Nevertheless, all experimental realizations of the MBL transition have relied on quasiperiodic disorder of optical lattices, necessitating a theoretical clarification of the quasiperiodic case. To this end, we employ the “TDVP” matrix product state algorithm of Haegeman et. al. (PRB 2016) to study the relaxation dynamics of local operators in both random and quasiperiodic systems at infinite temperature. In particular, we consider a nonintegrable spin chain and approach the MBL transition from the thermal phase by strengthening the disorder. Our preliminary work suggests that the effects of random and quasiperiodic disorder differ. In the random case, we find subdiffusive power law relaxation of the local energy consistent with Griffiths physics. In contrast, the quasiperiodic case exhibits slow, nonpowerlaw relaxation followed by a diffusive power law at late times. This suggests that, despite the initial slow dynamics, genuine Griffiths dynamics are absent in the quasiperiodic system. 
Friday, March 9, 2018 9:48AM  10:00AM 
X27.00008: Coexistence of Localized and Extended States in Disordered Systems Yixin Xiao, ZhaoQing Zhang, CheTing Chan It is well known that in disordered systems, Anderson localized states and extended states do not coexist at the same energy. Here we propose a simple mechanism to achieve the coexistence of localized and extended states both spectrally and spatially in a class of disordered quasi1D and quasi2D systems. The systems are partially disordered in a way that a few bands of extended states always exists, not affected by the randomness, whereas the states in all other bands become localized. The bands of extended states can overlap with those bands of localized states both in energy and in space, achieving the aforementioned coexistence. We demonstrate such coexistence in disordered multichain and multilayer systems. Such systems can be experimentally realized on multiple platforms such as cold atoms and optics. 
Friday, March 9, 2018 10:00AM  10:12AM 
X27.00009: ManyBody SelfLocalization in a TranslationInvariant Hamiltonian Rubem Mondaini, Zi Cai We study the statistical and dynamical aspects of a translationinvariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of manybody localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasiperiodic longrange interactions, which are now achievable in highfinesse cavity experiments, to find evidence suggestive of a divergent timescale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the groundstate of this system, being also present at infinite 
Friday, March 9, 2018 10:12AM  10:24AM 
X27.00010: Nonlinear Disordered Discrete Time Quantum Walks Ihor Vakulchyk, Mikhail Fistul, Pinquan Qin, Sergej Flach Discrete quantum walks (DQW) are a main tool in quantum computing research. At the same time, they are fascinating mathematical models on lattices with unitary operators involving only nearest neighbor coupling, and thus with a speedup in certain comptutations up to two orders of magnitude as compared to Hamiltonian based dynamics. I will introduce the translationally invariant DQW and its massive Dirac twoband structure. I will then introduce disorder and demonstrate the existence of, and control over Anderson localization [1]. Finally I will generalize the disordered DQW by adding nonlinear terms to the unitary operations. As a result, wave packet dynamics is characterized by a slow subdiffusive destruction of Anderson localization [2]. I will show that we can drive this process to unprecedented times as compared to previous studies. This will allow us to surpass the current computational horizon by a factor of up to 10^{3} and check whether the neverending subdiffusion IS keeping its universality beyond the hold horizons, or whether a slowing down effect will be seen as claimed in some publications. 
Friday, March 9, 2018 10:24AM  10:36AM 
X27.00011: Nonequilibrium phase diagram of a 1D quasiperiodic system with a singleparticle mobility edge Manas Kulkarni, Archak Purkayastha, Abhishek Dhar We investigate and map out the nonequilibrium phase diagram of a generalization of the well known AubryAndreHarper (AAH) model. This generalized AAH (GAAH) model is known to have a singleparticle mobility edge which also has an additional selfdual property akin to that of the critical point of AAH model. By calculating the population imbalance, we get hints of a rich phase diagram. We also find a fascinating connection between single particle wavefunctions near the mobility edge of GAAH model and the wavefunctions of the critical AAH model. By placing this model farfromequilibrium with the aid of two baths, we investigate the open system transport via system size scaling of nonequilibrium steady state (NESS) current, calculated by fully exact nonequilibrium Green's function (NEGF) formalism. The critical point of the AAH model now generalizes to a `critical' line separating regions of ballistic and localized transport. Like the critical point of AAH model, current scales subdiffusively with system size on the `critical' line. However, remarkably, the scaling exponent on this line is distinctly different from that obtained for the critical AAH model. A very interesting high temperature nonequilibrium phase diagram of the GAAH model emerges from our calculations. 
Friday, March 9, 2018 10:36AM  10:48AM 
X27.00012: Phasonic Spectroscopy of Tunable ColdAtom Quasicrystals Shankari Rajagopal, Ruwan Senaratne, Toshihiko Shimasaki, Peter Dotti, David Weld We describe and demonstrate a new spectroscopic probe of tunable quantum quasicrystals, realized with cold atoms in a quasiperiodic optical lattice. The formation, stability, excitation, and electronic structure of quasicrystals remain incompletely understood. In particular, phasonic modes (a quasicrystalline analogue of phonon modes) have important but poorlyunderstood effects on thermal and electronic transport in real quasicrystals. The extreme tunability of coldatom experiments enables a new technique for investigation of these open questions: coherent phasonic spectroscopy of tunable quantum quasicrystals. We present the first results from this new kind of lattice spectroscopy, measuring the effect of phasonic and phononic driving on an ultracold quantum gas in a quasiperiodic optical potential above and below the AubryAndre localization transition. 
Friday, March 9, 2018 10:48AM  11:00AM 
X27.00013: Local Integrals of Motion in the TwoSite AndersonHubbard Model Rachel Wortis, Malcolm Kennett, Brandon LeipnerJohns It has been proposed that the states of fully manybody 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 specic systems is nontrivial. We consider the disordered Hubbard model and by studying a small system provide concrete examples of the form of integrals of motion. We explore ways of identifying the most local choice with charge disorder alone and with both spin and charge disorder. 
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