Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session L50: Dynamics - Many Body Theory |
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Sponsoring Units: DCMP Chair: Hossein Dehghani, University of Maryland, College Park Room: Mile High Ballroom 1C |
Wednesday, March 4, 2020 8:00AM - 8:12AM |
L50.00001: Late time dynamics of dynamical correlation functions and out of time ordered correlators Jonathon Riddell, Álvaro Alhambra, Luis Garcia-Pintos, Erik Sorensen In this talk we study the universal properties of different types of dynamical quantites in time, for large classes of systems. First we investigate two-point correlation functions- also known as dynamical response functions in closed non-integrable many-body quantum systems. We show that for a large class of models these correlation functions factorize at late time, proving dissipation emerges from unitary dynamics. We similarly show that the fluctuations around the late time are bounded by the purity of the thermal ensemble. For auto-correlation functions we provide an upper bound on the timescale for which they equilibrate to this late time factorization. We then move onto study the late time dynamics of fermionic models in the presence of disorder for out of time ordered correlators. Focusing on the Aubry-André model we derive universal late time behavior for the OTOC in the extended regime of the model. These fermionic results are then used to extend the discussion to equilibration in finite time for all quadratic models in the extended regime. |
Wednesday, March 4, 2020 8:12AM - 8:24AM |
L50.00002: Self-averaging in many-body quantum systems out of equilibrium Lea Santos, Mauro Schiulaz, E. Jonathan Torres Herrera, Francisco Pérez-Bernal Despite its importance to experiments, numerical simulations, and the development of theoretical models, self-averaging in many-body quantum systems out of equilibrium remains underinvestigated. Usually, in the chaotic regime, self-averaging is just taken for granted. The numerical and analytical results presented here force us to rethink these expectations. They demonstrate that self-averaging properties depend on the quantity and also on the time scale considered. We show analytically that the survival probability in chaotic systems is not self-averaging at any time scale, even when evolved under full random matrices. We also analyze the participation ratio, Rényi entropies, the spin autocorrelation function from experiments with cold atoms, and the connected spin-spin correlation function from experiments with ion traps. We find that self-averaging holds at short times for the quantities that are local in space, while at long times, self-averaging applies for quantities that are local in time. Various behaviors are revealed at intermediate time scales. |
Wednesday, March 4, 2020 8:24AM - 8:36AM |
L50.00003: Measurement-induced entanglement dynamics in many-body localizable systems Oliver Lunt, Arijeet Pal In this work we explore the interplay of two types of entanglement transition: the many-body localization (MBL) transition, where eigenstates go from volume law to area law, and measurement-induced transitions, where recent work has demonstrated that the late-time entanglement entropy of random circuits can collapse from volume to area law above a finite critical measurement rate [1-3]. Whereas previous studies have focused mainly on random quantum circuits, here we focus on Hamiltonian dynamics. Many-body localizable systems exhibit at least two phases with distinct dynamical properties: the thermal and the localized phases. In this work, we investigate the effect of measurements on the entanglement dynamics of these phases. |
Wednesday, March 4, 2020 8:36AM - 8:48AM |
L50.00004: Quantum Impurity Far from Equilibrium: Quantum Transport Through a Dissipative Resonant Level Using DMRG Xin Zhang, Thomas Barthel, Harold U Baranger Using time-dependent matrix product state techniques, we study the quantum transport properties of a dissipative resonant level model, in which a quantum impurity is coupled to two leads and a bosonic bath. Experimentally, this model can be realized by coupling a quantum dot with resistive leads [1]. We focus on the far-from-equilibrium steady states. The non-linear I-V curves and their scaling behavior are presented for different dissipation strengths in the case of both symmetric and asymmetric coupling. In the symmetric setup, a quantum critical point of the two-channel Kondo class is present [2]. To probe properties of the quasiparticle excitations, which can be measured with tunneling spectroscopy, we study the spectral function and shot noise. |
Wednesday, March 4, 2020 8:48AM - 9:00AM |
L50.00005: Role of non-linear susceptibilities in non-equilibrium transport through an N-level Anderson impurity model away from half-filling Yoshimichi Teratani, Akira Oguri We study non-equilibrium SU(N) Kondo effect that occurs in quantum impurity systems at low-temperatures T and low-bias voltages eV. We expand the differential conductance up to terms of order T^{2} and (eV)^{2} at arbitrary electron fillings, using an extended version of the Fermi-liquid theory for the Anderson impurity model. The coefficients for these terms are determined by the linear and non-linear susceptibilities defined with respect to the equilibrium ground state [1,2]. We calculate these susceptibilities using the NRG for N=2, 4, and 6 in a wide range of electron fillings N_{d}, varying the impurity level position ε_{d}. The results show that contributions of the three-body susceptibilities on the transport coefficients increase as N_{d} deviates away from half-filling, especially near the fillings of N_{d} = 1 and N_{d} = N-1. We also employ a large N approach, i.e., the 1/(N-1) expansion with a scaling that keeps (N-1)U constant [3]. We find that the 1/(N-1) results and NRG results are in good already at N=4 and 6. |
Wednesday, March 4, 2020 9:00AM - 9:12AM |
L50.00006: Hamiltonian dynamics of a sum of interacting random matrices Matteo Bellitti, Siddhardh Morampudi, Christopher Laumann In ergodic quantum systems, physical observables have a non-relaxing component if they "overlap" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. |
Wednesday, March 4, 2020 9:12AM - 9:24AM |
L50.00007: Universal Dynamics of Stochastically Driven Quantum Impurities William Berdanier, Jamir Marino, Ehud Altman We show that the dynamics of a quantum impurity subject to a stochastic drive on one side and coupled to a quantum critical system on the other display a universal behavior inherited from the quantum critical scaling. Using boundary conformal field theory, we formulate a generic ansatz for the dynamical scaling form of the typical Loschmidt echo and corroborate it with exact numerical calculations in the case of a spin impurity driven by shot noise in a quantum Ising chain. We find that due to rare events the dynamics of the mean echo can follow very different dynamical scaling than the typical echo for certain classes of drives. Our results are insensitive to irrelevant perturbations of the bulk critical model and apply to all the microscopic models in the same universality class. |
Wednesday, March 4, 2020 9:24AM - 9:36AM |
L50.00008: Non-Equilibrium Dynamics of the SYK_{q=∞} Model Stefan Kehrein The Sachdev-Ye-Kitaev model is a paradigm for quantum many-body systems without a quasiparticle description. Its non-equilibrium dynamics after a quench was investigated in Ref. [1], where certain quenches to the q=∞ model could even be solved analytically. In this talk these analytical results are extended to arbitrary quenches to the q=∞ SYK model. Remarkably one always finds instant thermalization. |
Wednesday, March 4, 2020 9:36AM - 9:48AM |
L50.00009: Using charge- and spin-specific local integrals of motion to explore entanglement growth in the disordered Fermi Hubbard model Rachel Wortis, Brandon Leipner-Johns The Fermi Hubbard model has both charge and spin degrees of freedom at each site. We explore the coupling of the dynamics in these two channels in the presence of disorder. In particular, we write the Hamiltonian in terms of charge- and spin-specific local integrals of motion, and compare the strengths of the coupling constants linking integrals of motion of the same species (charge-charge and spin-spin) with those linking charge and spin. This provides an avenue to understanding the wide range of time scales which appear in the dynamics. |
Wednesday, March 4, 2020 9:48AM - 10:00AM |
L50.00010: Scalable probes of measurement-induced phase transitions David Huse, Michael Gullans Measurement-induced phase transitions are a recently uncovered class of critical phenomena that occur when many-body unitary dynamics are interspersed with measurements at a tunable rate. We uncover a local order parameter for such measurement-induced criticality (MIC) equal to the average entropy of a single reference qubit initially entangled with the system. Using this order parameter, we identify scalable probes of MIC that are immediately applicable to advanced quantum computing platforms. We test our proposal on a 1+1-dimensional stabilizer circuit model that can be classically simulated in polynomial time. We determine bulk and surface critical exponents of MIC for such models and find that they are very close, or equal to those of 2+0-dimensional critical percolation. Developing scalable probes of MIC in more general models may be a useful application of noisy-intermediate scale quantum (NISQ) devices, as well as point to more efficient realizations of fault-tolerant quantum computation. |
Wednesday, March 4, 2020 10:00AM - 10:12AM |
L50.00011: Higher-order and fractional discrete time crystals in clean long-range interacting systems Andrea Pizzi, Johannes Knolle, Andreas Nunnenkamp Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n>1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different 'higher-order' discrete time crystals with integer and, surprisingly, even fractional n>2. We characterize these non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions. |
Wednesday, March 4, 2020 10:12AM - 10:24AM |
L50.00012: Time dependent, external perturbations of Hubbard clusters with explicit many electron interactions and their implications Gayanath Fernando, Adil-Gerai Kussow, Kalum Palandage We examine the effects of harmonic and other time dependent external perturbations on a many electron system |
Wednesday, March 4, 2020 10:24AM - 10:36AM |
L50.00013: Flow Renormalization and Prethermal Regimes of Periodically-Driven Quantum Systems Martin Claassen One of the most fascinating aspects of non-equilibrium physics is that a quantum system pushed out of equilibrium can exhibit markedly different dynamics when probed on different time scales. We develop a flow renormalization approach for periodically-driven quantum systems, for which a rigorous relation between "flow time" and real time can be established. In this formalism, the dynamical problem is recast in terms of a flow towards an attractive thermal fixed point, while narrowly avoiding a series of unstable fixed points that determine distinct transient dynamical regimes at intermediate times. We show that a unique choice of flow permits relating flow-time and real-time evolution via analytic continuation, and study the appearance of long-lived prethermal regimes in Floquet Hubbard models and spin chains. |
Wednesday, March 4, 2020 10:36AM - 10:48AM |
L50.00014: Flow equation approach to periodically driven quantum systems Michael Vogl, Pontus Laurell, Aaron Barr, Gregory A Fiete We present a theoretical method to generate highly accurate time-independent Hamiltonians governing the finite-time behavior of time-periodic systems. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce effective Hamiltonians. The method has a range of validity reaching into frequency regimes that are usually inaccessible by high frequency expansions. Our approach is demonstrated for many-body Hamiltonians and offers an improvement over the more well-known Magnus expansion and the rotating frame approximation. We show how the method relates to the rotating frame approximation and how it can be used to approximately transform to a rotating frame when the exact transformation isn't tractable. We compare our approximate results to those found via exact diagonalization. |
Wednesday, March 4, 2020 10:48AM - 11:00AM |
L50.00015: Fermi-liquid corrections to non-equilibrium Keldysh vertex functions for an Anderson impurity model. Akira Oguri, Yoshimichi Teratani, Rui Sakano We study in detail the residual interaction between quasi-particles that plays an essential role in the non-equilibrium transport through quantum dots under finite bias voltage eV. Specifically, Fermi-liquid corrections to the vertex functions, which can be related to the collision integral for the Anderson impurity model, are calculated away from half-filling up to linear terms with respect to ω, ω', and eV at zero temperature T=0. Here, ω and ω' correspond to the energies of two interacting quasi-particles. The expansion coefficients are obtained by extending the recent developments [1,2], using the Ward-Takahashi identity for the Keldysh current vertex functions. We also discuss low-energy behavior of nonlinear current noise in the Fermi-liquid regime using the numerical renormalization group appraoch. |
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