Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session Y27: Disorder and Localization in AMO Systems II |
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Sponsoring Units: DAMOP DCMP Chair: Brian DeMarco, University of Illinois Urbana-Champaign Room: LACC 404B |
Friday, March 9, 2018 11:15AM - 11:27AM |
Y27.00001: Exploring one particle orbitals in large Many-Body Localized systems Benjamin Villalonga Correa, Xiongjie Yu, David Luitz, Bryan Clark Strong disorder in interacting quantum systems can give rise to Many-Body Localization (MBL), which defies thermalization due to the formation of an extensive number of quasi local integrals of motion. The one particle content of these integrals of motion is related to the one particle orbitals (OPOs) of the one particle density matrix, which shows a strong signature across the transition as pointed out by Bera et al. In this work we study the OPOs of eigenstates of an MBL system.We obtain accurate results for sizes up to L = 64. We find that the OPOs of eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, single MBL eigenstates at the mobility edge present two sets of qualitatively different OPOs, and so they are aware of the presence of an ergodic phase. Also, the OPOs decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find a 1/f distribution of the coupling constants of a certain range of the number operators of the OPOs, which is related to their exponential decay. |
Friday, March 9, 2018 11:27AM - 11:39AM |
Y27.00002: Energy Currents in the Disordered XYZ Spin Chain Scott Taylor, Maximilian Schulz, Christopher Hooley, Antonello Scardicchio The delocalized region preceding the many-body localization (MBL) transition is currently receiving a significant amount of attention due to apparent deviations from typical diffusive transport. The XXZ spin chain has been shown to exhibit subdiffusive spin transport at intermediate disorder strengths, and the nature of energy transport close to the MBL transition is still a matter of debate. |
Friday, March 9, 2018 11:39AM - 11:51AM |
Y27.00003: Superbosonization in disorder and chaos Tigran Sedrakyan, Konstantin Efetov Superbosonization formula aims at rigorously calculating fermionic integrals via employing supersymmetry. We derive such a supermatrix representation of superfield integrals and specify integration contours for the supermatrices. The derivation is essentially based on the supersymmetric generalization of the Itzikson-Zuber integral in the presence of anomalies in the Berezinian and shows how an integral over supervectors is eventually reduced to an integral over commuting variables. The approach is tested by calculating both one and two point correlation functions in a class of random matrix models. It is argued that the approach is capable of producing nonperturbative results in various systems with disorder, including physics of many-body localization, and other situations hosting localization phenomena. |
Friday, March 9, 2018 11:51AM - 12:03PM |
Y27.00004: Real-time dynamics of the subdiffusive random-field Heisenberg chain Christopher White, Sarang Gopalakrishnan, Gil Refael We investigate the dynamics of an ergodic random-field Heisenerg chain near the diffusive-subdiffusive transition. Previous work (Znidaric, Scardicchio, and Varma, PRL 117, 040601) has found subdiffusive conductivity in numerical experiments on non-equilibrium steady states. We use the matrix product density operator technique DMT to simulate the real-time evolution of long ($L \gtrsim 256$ sites) spin-1/2 chains; we measure not only global dynamical exponents consistent with the results of Znidaric, Scardicchio, and Varma, but also the spatial variation of these exponents. |
Friday, March 9, 2018 12:03PM - 12:15PM |
Y27.00005: Dephasing Catastrophe in 4-ε Dimensions: A Toy Model for the Ergodic to Many-Body-Localized Phase Transition Yunxiang Liao, Matthew Foster In this work, we propose a strategy to investigate the two-dimensional ergodic to many-body-localized (MBL) phase transition as a dephasing catastrophe by approaching from the ergodic side. In a closed interacting fermion system with quenched disorder, the dephasing of weak localization corrections to conductivity is caused by inelastic electron-electron collisions, which can be interpreted as interactions between electrons and thermal fluctuations of the hydrodynamic mode. For system with short-range interactions, the dephasing problem does not admit a closed-form solution due to the diffusive and non-Markovian nature of the fluctuations. It is reformulated as a geometric statistical-mechanical problem of a self-interacting polymer loop whose characteristic length scale is determined by the dephasing length. In the renormalization group framework, we study the critical behavior through a controlled epsilon expansion from the upper critical dimensions d=4. We find a nontrivial fixed point corresponding to temperature T*>0 where the dephasing rate vanishes. This critical point is associated with the toy version of ergodic-MBL transition in d=2 if it survives to ε=2. The analytical results reported here could be tested with a lattice polymer simulation. |
Friday, March 9, 2018 12:15PM - 12:27PM |
Y27.00006: Signatures of the Many-body Localized Regime in Two Dimensions Thorsten Wahl, Arijeet Pal, Steven Simon Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomena in one dimension using techniques of exact diagonalization and tensor networks. On the other hand, experiments in two dimensions have provided concrete results going beyond the previously numerically accessible limits while posing several challenging questions. We present |
Friday, March 9, 2018 12:27PM - 12:39PM |
Y27.00007: Loschmidt Echo in the Time Crystal Phase of Disordered Spin Systems Francisco Simão, Timo Mutas, Sebastian Paeckel, Markus Schmitt, Thomas Koehler, Salvatore Manmana Motivated by recent studies on systems exhibiting discrete time translational symmetry breaking (DTTSB) we investigate the Loschmidt echo for disordered spin systems with special focus on the transverse Ising model. Starting from the $Z_{2}$ symmetric limit we analytically obtain the time evolution for various short-ranged correlated initial states. Our results enable us to draw an intuitive picture for the emergence of DTTSB, from which we generalize our findings to systems with $Z_{n}$ symmetry breaking. |
Friday, March 9, 2018 12:39PM - 12:51PM |
Y27.00008: Disorder-Free Localization Adam Smith, Johannes Knolle, Roderich Moessner, Dmitry Kovrizhin The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the Hamiltonian, or through a special choice of a disordered initial state. Here, we present a family of very simple translationally invariant quantum models with only local interactions between spins and fermions. By identifying an extensive set of conserved quantities, we show that the system generates purely dynamically its own disorder, which gives rise to localization of fermionic degrees of freedom. Our work provides an answer to a decades old question whether quenched disorder is a necessary condition for localization. It also offers new insights into the physics of many-body localization, lattice gauge theories, and quantum disentangled liquids. |
Friday, March 9, 2018 12:51PM - 1:03PM |
Y27.00009: Anomalous transport in spin chains Vipin Kerala varma, Vadim Oganesyan, Antonello Scardicchio, Marko Znidaric, Clelia de Mulatier In this talk we report on anomalous transport of spin and energy in Heisenberg spin chains, at and away from the integrable limit using a variety of techniques (t-DMRG, eact diagonalization, memory functions) and models (quasiperiodic, disordered, weakly nonintegrable). We postulate a generic mechanism for such processes. |
Friday, March 9, 2018 1:03PM - 1:15PM |
Y27.00010: The effects of an impurity with auxilary motion Nathan Cheng, Mona Berciu When a light impurity is present in a lattice, the impurity may exhibit auxiliary motion to the lattice. We study the effects on the electronic spectrum and other properties of the material by the local oscillations of the impurity about its lattice equilibrium position (the impurity vibronic modes). These results are compared and contrasted for different electron couplings to the vibronic modes of the impurity, such as a Holstein-type coupling, where the vibronic modes modulate the on-site impurity energy, or a Peierls-type coupling, where the vibronic modes modulate the local hopping to the impurity. |
Friday, March 9, 2018 1:15PM - 1:27PM |
Y27.00011: Solvable Sachdev-Ye-Kitaev Models in Higher Dimensions: From Diffusion to Many-Body Localization Shaokai Jian, Hong Yao Many aspects of many-body localization (MBL) transitions remain elusive so far. Here, we propose a higher-dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model and show that it exhibits a MBL transition. The model on a bipartite lattice has N Majorana fermions with SYK interactions on each site of the A sublattice and M free Majorana fermions on each site of the B sublattice, where N and M are large and finite. For r = M/N < rc (rc=1), it describes a diffusive metal exhibiting maximal chaos. Remarkably, its diffusive constant vanishes as r → rc, implying a dynamical transition to a MBL phase. It is further supported by numerical calculations of level statistics which changes from Wigner-Dyson (r < rc) to Poisson (r > rc) distributions. Note that no subdiffusive phase intervenes between diffusive and MBL phases. Moreover, the critical exponent \nu = 0, violating the Harris criterion. Our higher-dimensional SYK model may provide a promising arena to explore exotic MBL transitions. |
Friday, March 9, 2018 1:27PM - 1:39PM |
Y27.00012: Driving induced many-body localization Eyal Bairey, Gil Refael, Netanel Lindner Subjecting a many-body localized system to a time-periodic drive generically leads to delocalization and a transition to ergodic behavior if the drive is sufficiently strong or of sufficiently low frequency. Here we show that a specific drive can have an opposite effect, taking a static delocalized system into the many-body localized phase. We demonstrate this effect using a one-dimensional system of interacting hardcore bosons subject to an oscillating linear potential. The system is weakly disordered, and is ergodic absent the driving. The time-periodic linear potential leads to a suppression of the effective static hopping amplitude, increasing the relative strengths of disorder and interactions. Using numerical simulations, we find a transition into the many-body localized phase above a critical driving frequency and in a range of driving amplitudes. Our findings highlight the potential of driving schemes exploiting the coherent suppression of tunneling for engineering long-lived Floquet phases. |
Friday, March 9, 2018 1:39PM - 1:51PM |
Y27.00013: On the stability of many-body localization in d>1 Ionut-Dragos Potirniche, Sumilan Banerjee, Ehud Altman It was recently argued that MBL is unstable in two and higher dimensions due to a thermalization avalanche triggerred by rare regions of weak disorder [1]. We test these arguments using exact diagonalization (ED) studies as well as a solvable effective model. The ED results show excellent agreement with a refined theory of the thermalization avalanche that includes the transient finite size effects, lending strong support to the avalanche scenario. At the same time, the solvable model we analyze suggests a possible mode of failure of the avalanche. In this scheme we model the finite ergodic region using a Sachdev-Ye-Kitaev model and couple it to an Anderson insulator of non-interacting fermions. In a suitable large-N limit, we find that the spectral function of a local operator changes dramatically when coupled to a large number of Anderson fermions and can even undergo a dynamical phase transition. While this fact does not in itslef preclude the thermalization avalanche, it violates a central assumption in the arguments of Ref. [1]. |
Friday, March 9, 2018 1:51PM - 2:03PM |
Y27.00014: Universal properties of many-body localization criticality in 1D quasiperiodic systems Shixin Zhang, Hong Yao The nature of many-body localization (MBL) transitions in 1D quasi-periodic systems remains illusive so far. We employ real-space renormalization group (RG) to investigate universal properties of such MBL transitions. By performing the state-of-the-art real-space RG analysis to systems with large size, our results show that the MBL transitions in 1D quasiperiodic systems have the critical exponent $\nu>2$ that exceeds the Harris-CCFS bound. Consequently, the MBL transitions in quasi-periodic 1D systems are stable against weak quenched random disorder. We also discuss several interesting features related to quasiperiodic-driven MBL systems. |
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