Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session B8: Quantum Many-Body Systems 1: Nonequilibrium Many Body Theory, Quenches, and Many Body Localization |
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Sponsoring Units: DCOMP Chair: Sarang Gopalakrishnan, CUNY College of Staten Island Room: 267 |
Monday, March 13, 2017 11:15AM - 11:27AM |
B8.00001: Eigenstate Thermalization and the fate of off-diagonal matrix elements in the two-dimensional transverse field Ising model Rubem Mondaini, Marcos Rigol The Eigenstate Thermalization Hypothesis (ETH) provides a framework that explain how thermalization happens in generic isolated quantum systems. The two-dimensional transverse field Ising model is one of the models that one can numerically verify its predictions and infer under which circumstances it is valid. To probe thermalization and its relationship with the onset of quantum chaos, we use full exact diagonalization in moderately sized lattices using symmetries. We examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. An analysis of finite size effects reveals that quantum chaos and eigenstate thermalization occur in those systems whenever the transverse field is nonvanishing and not too large, that is, away from the integrable limits. Going beyond this analysis, we investigate the behavior of off-diagonal matrix elements of few-body operators in the eigenstate basis of the Hamiltonian. With this we can infer its relationship with the predictions of equivalent quantities in random matrix theory. Reference: R. Mondaini, K. R. Fratus, M. Srednicki, and M. Rigol, ``Eigenstate thermalization in the two-dimensional transverse field Ising model'', Phys. Rev E, {\bf 93}, 032104 (2016). [Preview Abstract] |
Monday, March 13, 2017 11:27AM - 11:39AM |
B8.00002: Canonical Universality Anatoly Dymarsky Isolated quantum system in a pure state may be perceived as thermal if only substantially small fraction of all degrees of freedom is probed. We propose that in a chaotic quantum many-body system all states with sufficiently small energy fluctuations are approximately thermal. We refer to this hypothesis as Canonical Universality (CU). This hypothesis generalizes the Eigenstate Thermalization Hypothesis (ETH) which proposes that for such systems individual energy eigenstates are thermal. Integrable and BML systems do not satisfy CU. We provide theoretical and numerical evidence supporting the CU hypothesis. [Preview Abstract] |
Monday, March 13, 2017 11:39AM - 11:51AM |
B8.00003: Dynamics of the transverse-field Ising model in 3D Markus Schmitt, Markus Heyl We formulate the dynamics after a quench in the three-dimensional transverse-field Ising model in terms of classical partition sums, which can be evaluated using conventional Monte Carlo methods for classical spin systems with system sizes markedly beyond the capabilities of, e.g., exact diagonalization. In this way, we obtain insights into the time evolution of observables and dynamical quantum phase transitions in the Loschmidt echo, which we analyze in the vicinity of critical times similar to [M. Heyl, Phys. Rev. Lett. 115, 140602 (2015)]. [Preview Abstract] |
Monday, March 13, 2017 11:51AM - 12:03PM |
B8.00004: Critical Properties of the Many-Body Localization Transition Vedika Khemani, Say-Peng Lim, Donna Sheng, David Huse The transition from a many-body localized phase to a thermalizing one is a dynamical quantum phase transition which lies outside the framework of equilibrium statistical mechanics. We provide a detailed study of the critical properties of this transition at finite sizes in one dimension. We find that the entanglement entropy of small subsystems looks strongly subthermal in the quantum critical regime, which indicates that it varies discontinuously across the transition as the system-size is taken to infinity, even though many other aspects of the transition look continuous. We also study the variance of the half-chain entanglement entropy which shows a peak near the transition, and find that the sample-to-sample variations in this quantity are larger than the intra-sample variations across eigenstates and spatial cuts. We posit that these results are consistent with a picture in which the transition to the thermal phase is driven by an eigenstate-dependent sparse resonant ``backbone'' of long-range entanglement, which just barely gains enough strength to thermalize the entire system on the thermal side of the transition as the system size is taken to infinity. This discontinuity in a global quantity --- the presence of a fully functional bath --- in turn implies a discontinuity even for local properties. We discuss how this picture compares with existing renormalization group treatments of the transition. [Preview Abstract] |
Monday, March 13, 2017 12:03PM - 12:15PM |
B8.00005: Operator Spreading and Scrambling in a Quantum Chaotic Spin Chain Cheryne Jonay, David. A Huse We numerically examine operator dynamics under the unitary time evolution of a quantum chaotic Ising spin chain with longitudinal and transverse fields. We study the spreading of initially local operators. We also focus on the scrambling of the operators, asking: at late time, to what extent do time-evolved local operators statistically resemble random operators? Does the leading edge of the operator spreading move faster than the scrambling of the operator? How many different time regimes are there in the spreading and scrambling of a local operator in a finite quantum chaotic spin chain? [Preview Abstract] |
Monday, March 13, 2017 12:15PM - 12:27PM |
B8.00006: Simple Heuristics for Quantum Entanglement Growth Adam Nahum, Jonathan Ruhman, Sagar Vijay, Jeongwan Haah A quantum many-body system, prepared initially in a state with low entanglement, will entangle distant regions dynamically. How does this happen? I will discuss entanglement entropy growth for quantum systems subject to random unitary dynamics -- i.e. Hamiltonian evolution with time-dependent noise, or a random quantum circuit. I will show how entanglement growth in this ‘noisy’ situation exhibits universal structure, which in 1D is related to the Kardar-Parisi-Zhang equation. I will also argue that understanding entanglement growth for random dynamics leads to heuristic pictures that apply to more general (i.e. non-noisy) dynamics, both in 1D and in higher dimensions. [Preview Abstract] |
Monday, March 13, 2017 12:27PM - 12:39PM |
B8.00007: A possible non-ergodic metallic phase in a system with single-particle mobility edge Xiao Li, Xiaopeng Li Signatures of many-body localization have been recently demonstrated in cold-atom experiments using a one-dimensional incommensurate lattice potential. It is often believed that such a system is well captured by the 1D fermionic Aubry-Andre model. However, there is a marked difference between these two models: the incommensurate lattice model is known to have a single-particle mobility edge, while the Aubry-Andre model does not. In this work we derive an effective tight-binding model for atoms in a one-dimensional incommensurate lattice potential, and show that the corrections to the Aubry-Andre model are vital to capture the existence of a single-particle mobility edge. We further demonstrate that in a small system the single-particle mobility edge survives electron-electron interactions, giving rise to a possible non-ergodic metallic phase. [Preview Abstract] |
Monday, March 13, 2017 12:39PM - 12:51PM |
B8.00008: Holographic entanglement entropy for generic quantum many-body systems Stefan Kehrein The Ryu-Takayanagi conjecture [1] about the holographic derivation of the entanglement entropy provides a remarkable geometric picture by relating minimal surfaces to the entanglement entropy. Underlying this conjecture is the AdS/CFT correspondence, which limits the applicability of this geometric picture in its original formulation to a very specific set of theories. In this talk I will show how the flow equation method [2,3] can be used to construct an emergent geometric picture for eigenstates of generic quantum many-body systems in a weak link limit. Explicit results for the entanglement entropy of fermionic systems in d=1,2,3 dimensions are calculated and compared with known results. The method yields the correct area law with/without logarithmic corrections for ground states of critical/gapped systems. I also discuss the crossover to a volume law for excited states, which comes about very naturally in the flow equation framework. \newline [1] S. Ryu and T. Takayanagi, Phys. Rev. Lett. 96, 181602 (2006) \newline [2] F. Wegner, Ann. Phys. (Leipzig) 3, 77 (1994) \newline [3] S. Kehrein, The Flow Equation Approach to Many-Particle Systems (Springer, 2006) [Preview Abstract] |
Monday, March 13, 2017 12:51PM - 1:03PM |
B8.00009: Imaginary Time Dynamics of Low Energy States in Quantum Many-Body Hamiltonians Phillip Weinberg, Anders Sandvik Here we use imaginary time dynamics to extract the dynamic exponent $z$ of Quantum many-body Hamiltonians $H$ which have a ground state with long range order. This is done by evolving an excited state in imaginary time (e.g. with $e^{-\tau H}$) and measuring the time it takes for the state to relax to the ground state. We derive a generic finite size scaling theory which shows that this relaxation time diverges as $L^z$ where $z$ is the dynamic exponent of the low energy state(s). This scaling theory is then used to develop a systematic way of numerically extracting the dynamic exponent from finite size data. Using Quantum Monte Carlo to numerically simulate imaginary time, we apply this method to spin-1/2 Heisenberg Anti-ferromagnets on two different lattice geometries: A 2-dimensional square lattice, and a site diluted square lattice at the percolation threshold. For the 2-dimensional square lattice we recover $z=2.001(5)$, which is consistent with the known values $z=2$. While for the site dilute Heisenberg model we find that the dynamic exponent is $z=3.90(1)$ or $z=2.055(8)D_f$ where $D_f$ is the fractal dimension of the lattice. This is an improvement on previous estimates of $z\approx 3.7(1)$. [Preview Abstract] |
Monday, March 13, 2017 1:03PM - 1:15PM |
B8.00010: Open Wilson chains for quantum impurity models: Keeping track of all bath modes Jan von Delft, Benedikt Bruognolo, Nils-Oliver Linden, Frauke Schwarz, Katharina Stadler, Andreas Weichselbaum, Frithjof B. Anders, Matthias Vojta When constructing a Wilson chain to represent a quantum impurity model, the effect of truncated bath modes is neglected. We show that their influence can be kept track of systematically by constructing an ``open Wilson chain'' in which each site is coupled to a separate effective bath of its own. This strategy enables us to cure the so-called mass-flow problem that can arise when using standard Wilson chains to treat impurity models with asymmetric bath spectral functions at finite temperature. We demonstrate this for the strongly sub-Ohmic spin-boson model at quantum criticality where we directly observe the flow towards a Gaussian critical fixed point. [Preview Abstract] |
Monday, March 13, 2017 1:15PM - 1:27PM |
B8.00011: Comparative study of impurity solvers for Dynamical Mean Field Theory Mancheon Han, Hyungju Oh, Choong-Ki Lee, Hyoung Joon Choi The dynamical mean field theory (DMFT), which maps interacting electrons in solid to a single-impurity Anderson model (SIAM) is a methodology to study correlated electron systems. To perform DMFT approach, one needs a numerical method to solve the mapped impurity problem. Among various methods, we implemented three impurity solvers. The first one is the iterative perturbation theory (IPT), which approximates the self-energy by its second order perturbation expansion. It can be conducted within very short time and gives real-frequency quantities without any post-process. Second, we considered the exact diagonalization (ED) method, which approximates infinite bath in SIAM to some finite number of states. Lastly, we implemented the hybridization-expansion continuous-time quantum Monte Carlo (CT-HYB). It is numerically exact in the imaginary frequency, and analytic continuation is needed to get real-frequency quantities like spectral functions. Using three solvers, we calculated physical properties of several systems from simple models to real materials and compared the results. This work was supported by NRF of Korea (Grant No. 2011-0018306) and KISTI supercomputing center (Project No. KSC-2016-C3-0052). [Preview Abstract] |
Monday, March 13, 2017 1:27PM - 1:39PM |
B8.00012: Nonequilibrium steady-state transport through quantum impurity models -- a hybrid NRG-DMRG treatment Frauke Schwarz, Jan von Delft, Andreas Weichselbaum Matrix Product State (MPS) methods, and in particular the Numerical Renormalization Group (NRG), have proven to be successful in describing interacting impurity models in equilibrium. For steady-state nonequilibrium, arising e.g. due to an applied voltage, we suggest to combine NRG with the Density Matrix Renormalization Group (DMRG): NRG is used to deal with virtual transitions to high-lying excitations, leading to a renormalized impurity problem, whereas DMRG is used to treat the nonequilibrium dynamics of the remaining low-lying excitations. Furthermore, we use a basis in which the thermal state of the noninteracting leads (decoupled from the impurity) is described by a product state resulting in a comparatively low entanglement. These two ideas enable us to deduce steady-state expectation values for the nonequilibrium Single Impurity Anderson Model (SIAM) based on quench calculations. In particular, we study the splitting of the Kondo resonance in the zero-bias peak as a function of increasing magnetic field. While our approach allows us to directly focus on the relevant low-energy regime in a properly designed closed system, it is also naturally suited to be extended to a truly open system by introducing Lindblad driving terms [F. Schwarz et al., PRB 94, 155142] [Preview Abstract] |
Monday, March 13, 2017 1:39PM - 1:51PM |
B8.00013: Non-equilibrium transport in the quantum dot: quench dynamics and non-equilibrium steady state Adrian Culver, Natan Andrei We present an exact method of calculating the non-equilibrium current driven by a voltage drop across a quantum dot. The system is described by the two lead Anderson model at zero temperature with on-site Coulomb repulsion and non-interacting, linearized leads. We prepare the system in an initial state consisting of a free Fermi sea in each lead with the voltage drop given as the difference between the two Fermi levels. We quench the system by coupling the dot to the leads at $t=0$ and following the time evolution of the wavefunction. In the long time limit a new type of Bethe Ansatz wavefunction emerges, which satisfies the Lippmann-Schwinger equation with the two Fermi seas serving as the boundary conditions. This exact, non-perturbative solution describes the non-equilibrium steady state of the system. We describe how to use this solution to compute the infinite time limit of the expectation value of the current operator at a given voltage, which would yield the I-V characteristic of the dot. [Preview Abstract] |
Monday, March 13, 2017 1:51PM - 2:03PM |
B8.00014: Scrambling and onset of chaos in quantum many-body systems Debanjan Chowdhury, Brian Swingle The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We have studied the onset of scrambling in two broad classes of systems: for interacting systems with static disorder, and, for the (2 + 1)-dimensional O(N) non-linear sigma-model. We find generically that in the first class of systems we considered, disorder slows the onset of scrambling [1], and, in the case of a many-body localized (MBL) state, partially halts it. We also conjecture on the growth of commutators in a weakly interacting diffusive metal. In the second class of systems, we considered the O(N) model in thermal equilibrium at a temperature $T$ above the zero temperature quantum critical point. The relevant commutators grow exponentially in time with a rate denoted $\lambda_L$. We find $\lambda_L = c T/N$ to leading order in 1/N, where $c$ is a universal constant [2]. We also comment on the growth of commutators in space as measured by the butterfly velocity. [1] B. Swingle & D. Chowdhury, arXiv:1608.03280 [2] D. Chowdhury & B. Swingle, to appear [Preview Abstract] |
Monday, March 13, 2017 2:03PM - 2:15PM |
B8.00015: Quantum thermalization and the expansion of atomic clouds Louk Rademaker In the traditional 19th century approach to thermodynamics, one studies whether a system will reach thermal equilibrium when brought into contact with an infinitely big heat bath. In this talk, I will discuss this problem in the context of quantum many-body systems. Surprisingly, even noninteracting fermionic and bosonic systems will thermalize, as one can explicitly infer from computing the time-dependent modular Hamiltonian. The approach to thermalization is of a ballistic nature for fermions, $\Delta E \sim t^{-d}$ where $d$ is the dimension. Bosons, on the other hand, smoothly change from ballistic at high bath temperatures to diffusive $\Delta E \sim t^{-d/2}$ behavior at low temperatures. Finally, I will discuss how to compute the thermalization in generic interacting non-integrable systems, thereby presenting some numerical results for the interacting Bose-Hubbard model in one dimension. [Preview Abstract] |
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