Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session K25: Disorder and Localization in AMO Systems II: Manybody LocalizationFocus

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Sponsoring Units: DAMOP DCMP Chair: Michael Kolodrubetz, University of Texas at Dallas Room: BCEC 160A 
Wednesday, March 6, 2019 8:00AM  8:12AM 
K25.00001: ConfigurationControlled ManyBody Localization and the Mobility Emulsion Michael Schecter, Thomas Iadecola, Sankar Das Sarma We uncover a new nonergodic phase, distinct from the full MBL phase, in a disordered twoleg ladder of interacting hardcore bosons. The dynamics of this emergent phase is determined by the manybody configuration of the initial state and features the coexistence of localized and extended manybody states at fixed energy density. We show that eigenstates in this phase can be described in terms of interacting emergent Ising spin degrees of freedom suspended in a mixture with inert chargelike degrees of freedom (doublons), and thus dub it a mobility emulsion (ME). We argue that grouping eigenstates by their doublon density reveals a transition between localized and extended states that is invisible as a function of energy density. We further demonstrate that the dynamics of the system following a quench may exhibit either thermalizing or localized behavior depending on the doublon density of the initial product state. These results establish a new paradigm for using manybody configurations as a tool to study and control nonergodic dynamics which can be realized in existing disordered BoseHubbard ladders. 
Wednesday, March 6, 2019 8:12AM  8:48AM 
K25.00002: Manybody localization and the localization transition in quasiperiodic potentials Invited Speaker: Ulrich Schneider Quasiperiodic potentials, in particular AubryAndretype models, have routinely been employed by us and others as substitutes for real random disorder in the study of manybody localization with ultracold atoms. Far away from the transition, the resulting localized phases are indeed expected to be essentially identical. However, quasiperiodic potentials are not random but longrange ordered. Hence their physics must ultimately be very different. For instance, they do not contain any rare region and, as a result, the nature of the localization transition could be entirely different. 
Wednesday, March 6, 2019 8:48AM  9:00AM 
K25.00003: Beyond many body localization: A Hamiltonian with simultaneous area law and log law eigenstates. Di Luo, Xiongjie Yu, Bryan Clark A prime characterization of manybody localized (MBL) systems is the entanglement of their eigenstates; in contrast to the typical ergodic phase whose eigenstates are volume law, MBL eigenstates obey an area law. In this work, we show that a spindisordered Hubbard model has both a large number of arealaw eigenstates as well as a large number of eigenstates whose entanglement scales logarithmically with system size (loglaw). This model, then, is a microscopic Hamiltonian which is neither ergodic nor manybody localized. We establish these results through a combination of analytic arguments based on the etapairing operators combined with a numerical analysis of eigenstates. In addition, we describe and simulate a dynamic time evolution approach starting from product states through which one can separately probe the area law and loglaw eigenstates in this system. 
Wednesday, March 6, 2019 9:00AM  9:12AM 
K25.00004: Probing Entanglement in a ManyBodyLocalized System Robert Schittko, Alexander Lukin, Matthew Rispoli, Ming E Tai, Adam Kaufman, Soonwon Choi, Vedika Khemani, Julian Leonard, Markus Greiner An interacting quantum system that is subject to disorder may cease to thermalize due to localization of its constituents, thereby marking the breakdown of thermodynamics. The key to our understanding of this phenomenon lies in the system's entanglement, which is experimentally challenging to measure. We realize such a manybodylocalized system in a disordered BoseHubbard chain and characterize its entanglement properties through particle fluctuations and correlations. We observe that the particles become localized, suppressing transport and preventing the thermalization of subsystems. Notably, we measure the development of nonlocal correlations, whose evolution is consistent with a logarithmic growth of entanglement entropy  the hallmark of manybody localization. Our work experimentally establishes manybody localization as a qualitatively distinct phenomenon from localization in noninteracting, disordered systems. 
Wednesday, March 6, 2019 9:12AM  9:24AM 
K25.00005: Manybody localization as a large family of localized ground states Maxime Dupont, Nicolas Macé, Nicolas Laflorencie It is wellknown that ManyBody Localized (MBL) eigenstates are only arealaw entangled, even at high energy, although it is the usual hallmark of ground states of shortrange Hamiltonians. It is therefore legitimate to ask whether zerotemperature physics may have some connections with MBL states. Building on this simple idea, we ask whether an arbitrary MBL state could also be the ground state of another Hamiltonian? This question falls in the more general following problem: given a single eigenstate, does it uniquely encode the underlying Hamiltonian? Using large scale DMRG simulations [1], we show that in the presence of disorder, a localized ground state is a very good approximation for an MBL excited state of a different Hamiltonian that differs only by its local disorder configuration. Following similar ideas, we also investigate [2] the ergodic  MBL transition at high energy using standard shiftinvert exact diagonalization techniques. 
Wednesday, March 6, 2019 9:24AM  9:36AM 
K25.00006: KosterlitzThouless scaling at manybody delocalization phase transitions Philipp Dumitrescu, Siddharth A Parameswaran, Anna Goremykina, Maksym Serbyn, Romain Vasseur We propose a scaling theory for the manybody localization (MBL) phase transition in one dimension, building on the idea that the transition proceeds via a `quantum avalanche'. The critical properties are captured at a coarsegrained level by a KosterlitzThouless renormalization group flow. Based on this scaling picture, there are different scenarios for the behavior of fractal rare thermal inclusions within the MBL phase. We propose that the nearcritical MBL phase could host rare thermal regions that are powerlaw distributed in size. This points to the existence of a second transition within the MBL phase, at which these powerlaws change to a stretched exponential form. Large scale numerical simulations of a phenomenological models capturing the critical properties near the MBL transition support this picture. 
Wednesday, March 6, 2019 9:36AM  9:48AM 
K25.00007: Quantum coherence, phases of matter and manybody localization Lorenzo Campos Venuti, Paolo Zanardi Quantum coherence is one of the most fundamental traits of quantum mechanics. The coherence generating power (CGP) is the ability of a quantum unitary map of generating coherence. It is defined as the average coherence produced by the map applied to the set of incoherent states. In this talk I will report upon an unexpected link between these information theoretic concepts, and well known condensed matter quantities. Given two point in the phase diagram of a system one can ask about the CGP of the adiabatic intertwiner connecting the two points. The CGP turns out to be the inverse participation ratio, a quantity used to detect manybody localization (MBL) while for closeby points the CGP is exactly given by the d.c. dielectric polarizability. Using know results we are able to show that, in the thermodynamic limit, the CGP becomes maximal in the ergodic phase and submaximal in the MBL phase while the differential coherence diverges in the ergodic and subdiffusive phase while it tends to a constant in the MBL phase. 
Wednesday, March 6, 2019 9:48AM  10:00AM 
K25.00008: Global and shortrange entanglement properties in excited, manybody localized spin chains Colin West, TzuChieh Wei We explore the use of shortrange entanglement measures, such as concurrence and negativity, and global entanglement measures such as geometric entanglement, as indicators of manybody localization (MBL) in the spectra of disordered spin systems. From the perspective of entanglement monogamy, the two types of entanglement behave oppositely in the thermalized and MBL phases. In a recent work, the concurrence of subsystems, a measure of local entanglement, was used in a study of manybody localization in a onedimensional spin1/2 system (Bera and Lakshminarayan, 2016). We show numerically that the negativity displays notably similar behavior for this system, with the advantage that it can also be extended to systems of higher local dimension. We then demonstrate this extension in practice by using it to predict the existence of an MBL phase in a disordered a spin1 system. In terms of global entanglement, the geometric entanglement of both spin1/2 and spin1 systems is also shown to behave as a complementary indicator of the MBL phenomenon. 
Wednesday, March 6, 2019 10:00AM  10:12AM 
K25.00009: Multiscale entanglement clusters at the manybody localization phase transition Loic Herviou, Soumya Bera, Jens Bardarson We study numerically the formation of entanglement clusters across the manybody localization phase transition. 
Wednesday, March 6, 2019 10:12AM  10:24AM 
K25.00010: Universality class of manybody localization transition on 1D system with both random and quasiperiodic potentials Shixin Zhang, Hong Yao Whether MBL transitions in quasiperiodic (QP) and random systems belong to the same universality class or two distinct ones has not been decisively resolved so far. Here we investigate MBL transitions in onedimensional (d=1) QP systems as well as in random systems by stateoftheart realspace renormalization group (RG) calculation. Our realspace RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent $\nu\approx 2.4$, which respects the HarrisLuck bound ($\nu>1/d$) for QP systems. Note that $\nu\approx 2.4$ for QP systems also satisfies the HarrisCCFS bound ($\nu>2/d$) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. By investigating the system with both QP and random potentials via realspace RG, we directly show that the QPinduced MBL criticality is robust against small randomness. Consequently, our realspace RG results imply that there are indeed two stable universality classes of MBL criticalities. We further discuss the possible scenario of the global phase diagram with both types of MBL transitions. 
Wednesday, March 6, 2019 10:24AM  10:36AM 
K25.00011: Constructing local integrals of motion in the manybody localized phase Vipin Kerala varma, Vadim Oganesyan, David Pekker, Abhishek Raj, Sarang Gopalakrishnan We consider a manybody localized spin system and its description by the socalled lbit Hamiltonian. We outline a renormalization flow procedure to construct the extensive set of conserved quantities, and demonstrate that their locality results in exponentially decaying interactions in this effective model. The associated localization length of this decay is shown to manifest properties very similar to the noninteracting case of Anderson localization: normality of its distribution across samples, and its direct qualitative correspondence to the local spectral properties. A numerical simulation of a magnetic spinecho protocol quantitatively reproduces these theoretically computed length scales. We therefore argue that these local integrals of motion help to practically identify the manybody localized phase. 
Wednesday, March 6, 2019 10:36AM  10:48AM 
K25.00012: Apparent slow dynamics in the ergodic phase of a driven manybody localized system without extensive conserved quantities Talía Lezama Mergold Love, Soumya Bera, Jens Bardarson We numerically study the dynamics on the ergodic side of the manybody localization transition in a Floquet model with no global conservation laws. We describe and employ a numerical technique based on the fast WalshHadamard transform that allows us to perform an exact time evolution for large systems and long times. As in models with conserved quantities we observe a slowing down of the dynamics as the transition into the manybody localized phase is approached. More specifically, our data is consistent with a subballistic spread of entanglement and a stretchedexponential decay of the return probability, with the appropriately defined exponents, for a fixed system size, seeming to smoothly go to zero at the transition. However, with access to larger system sizes, we observe a clear flow of the exponents towards faster dynamics and can not rule out that the slow dynamics is a finitesize effect. Furthermore, we observe examples of nonmonotonic dependence of the exponents with time, with dynamics initially slowing down but accelerating again at even larger times, reminiscent of what is observed in large scale simulations of random regular graphs and consistent with the slow dynamics being a crossover phenomena with a localized critical point. 
Wednesday, March 6, 2019 10:48AM  11:00AM 
K25.00013: Phase diagram and observables of manybody localization in transmon circuit arrays Tuure Orell, Alexios Michailidis, Maksym Serbyn, Matti Silveri Disordered interacting quantum systems can undergo a phase transition from ergodic to manybody localized phase. Most of the previous theoretical studies on this subject concentrate on spin systems, and this phenomenon has been observed e.g. in optical lattices with ultracold atoms. In this work, we investigate the potential use of superconducting transmon circuits as a platform for experimental studies of the manybody localization [1]. We study numerically onedimensional disordered arrays of up to 14 transmons, and find that the phase transition occurs at experimentally realizable values of disordered onsite potentials and is robust against experimentally relevant perturbations such as weak nextnearest neighbor and higherorder Kerr interactions. Based on the simulations of the system dynamics, we find that the temporal fluctuations of transmon occupations could be used as an observable for probing the manybody localization in transmon circuits. 
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