Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session B43: Precision many-body physics II: Dynamics of 1D quantum systemsFocus
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Sponsoring Units: DCOMP DAMOP DCMP Chair: Guy Cohen, Tel Aviv University Room: 702 |
Monday, March 2, 2020 11:15AM - 11:51AM |
B43.00001: Quantum Phase Transitions Go Dynamical Invited Speaker: Victor Gurarie Just like a thermal partition function can be a nonanalytic function of temperature, the trace of the evolution operator of a quantum system can be a nonanalytic function of time, the phenomenon referred to as dynamical quantum phase transitions. These singularities which occur at certain points in time in the evolution of a quantum system are the subject of this talk. Interestingly, they can even appear in systems which do not undergo conventional thermal or quantum phase transitions, although precise criteria when they are expected to occur are not yet known. While there might be no obvious way to measure the trace of the evolution operator directly, it is possible to observe the “return probability”, the probability that a system which underwent a quantum quench and subsequently evolved for some time finds itself back in its original state. Sharing some similarity with the trace of the evolution operator, this probability can also be singular at certain times. In the context of quantum quench dynamics these singularities were already observed experimentally. Interpreting the trace of the evolution operator in terms of spectral form factors allows to further narrow down the class of quantum systems which could feature these singularities. In particular, they can be seen in integrable and many body localized systems which can have appropriate spectral form factors, although they are not limited to these types of systems. In the absence of a comprehensive theory of these singularities, their numerical study is often the only tool at our disposal to identify relevant systems where they may be present. |
Monday, March 2, 2020 11:51AM - 12:03PM |
B43.00002: Information measures for local quantum phase transitions: Lattice bosons in a one-dimensional harmonic trap Yicheng Zhang, Lev Vidmar, Marcos Rigol We study ground-state quantum entanglement in the 1D Bose-Hubbard model in the presence of a harmonic trap. We focus on two transitions that occur upon increasing the characteristic particle density: the formation of a Mott insulating domain with site occupation one at the center of the trap (lower transition), and the emergence of a superfluid domain at the center of the Mott insulating one (upper transition). These transitions generate discontinuities in derivatives of the total energy and have been characterized by local (nonextensive) order parameters, so we refer to them as local quantum phase transitions. We show that while a second derivative of the total energy is continuous with a kink at the lower transition, it is discontinuous at the upper transition. We also show that bipartite entanglement entropies are order parameters for those local quantum phase transitions. We use the density matrix renormalization group, and show that the transition points extracted from entanglement measures agree with the predictions of the local density approximation in the thermodynamic limit. We discuss how to determine the transition points from results in small systems, such as the ones realized in recent optical lattice experiments that measured the order-2 Renyi entanglement entropy. |
Monday, March 2, 2020 12:03PM - 12:15PM |
B43.00003: Low-energy physics in the critical phase of the bilinear-biquadratic spin-1 chain Moritz Binder, Thomas Barthel We use an efficient density matrix renormalization group (DMRG) algorithm to compute precise dynamic structure factors for the bilinear-biquadratic spin-1 chain with Hamiltonian H = Σi [cosθ (Si * Si+1) + sinθ (Si * Si+1)2]. Here, we focus on explaining the physics in the extended critical phase (π/4 ≤ θ < π/2) of the model. The phase transition from the Haldane phase to the critical phase is marked by the SU(3)-symmetric ULS point (θ = π/4), where the elementary excitations are spinons that can be obtained from the Bethe ansatz solution. As we move deeper into the critical phase, the spinon continua contract, and new striking features appear at higher energies. In the vicinity of the transition point from the critical to the ferromagnetic phase, a dispersion with a surprisingly simple functional form emerges, suggesting integrability of the model in the limit θ → π/2-. |
Monday, March 2, 2020 12:15PM - 12:27PM |
B43.00004: Entanglement decomposition for the simulation of quantum many-body dynamics Thomas Barthel Nonequilibrium dynamics in quantum matter are at the frontier of current research. Efficient and precise simulation techniques are needed to improve our understanding of equilibration and thermalization, dynamical phase transitions, decoherence effects, quantum transport etc. A major obstacle is the growth of entanglement with time which generally implies an increased complexity of the quantum state. For instance, the computation costs of simulations based on tensor network states generally grow rapidly in time, limiting the maximum reachable times. I will show how this problem can be addressed through entanglement decomposition. We can follow the dynamics, starting from an initial state, until the entanglement has grown to a point where our simulation resources are exhausted. We then decompose the current state into lower entangled components and continue by simulating the evolution of these components, decomposing them again when needed. I will demonstrate a specific entanglement decomposition scheme for matrix product state simulations and discuss its efficiency for the study of dynamics in quantum magnets. |
Monday, March 2, 2020 12:27PM - 12:39PM |
B43.00005: Energy resolved many-body localization emulated with a superconducting quantum processor Chen Cheng, Qiujiang Guo, Zhenghang Sun, Rubem Mondaini, Heng Fan, Haohua Wang Many-body localization (MBL) describes the regime where isolated matter in disorder environments is able to retain local quantum information at arbitrarily long times, evading thermal equilibrium that naturally occurs in generic quantum systems under their own dynamics. In most experimental studies, MBL has been investigated in various highly-controlled environments, ranging from ultracold atoms in optical lattices, trapped ions to, more recently, quantum processors implemented via superconducting qubits. In this work, taking advantages of the large degree of tunability of the latter platform and using up to 19 qubits, we report on an energy resolved MBL transition. Specifically, by preparing generic product states with different energies and monitoring the persistence of local information in real time dynamics, we are able, for the first time, to investigate the MBL transition at different energy densities, and show an energy resolved experimental MBL phase diagram. While controversies on the existence of many-body mobility edge still exist, due to the system fineteness amenable to classical computers, our investigation potentially opens a path to the final answer by direct quantum simulations. |
Monday, March 2, 2020 12:39PM - 12:51PM |
B43.00006: Exact two-spinon contribution to the longitudinal dynamical structure factor of the anisotropic XXZ model with comparison to DMRG simulations Andreas Weichselbaum, Igor Zaliznyak, Isaac P. Castillo, Jean-Sébastien Caux Motivated by inelastic neutron scattering experiments on quasi-one dimensional XXZ systems such as Yb2Pt2Pb, an exact formula for the two-spinon contribution to the dynamical structure factor is developed based on the quantum group (QG) approach. The results provide a QG derivation of the Baxter formula for the T=0 ordered spin. They are consistent with sum rules, and in excellent agreement with Density Matrix Renormalization Group (DMRG) simulations. |
Monday, March 2, 2020 12:51PM - 1:03PM |
B43.00007: Nonequilibrium steady state of quantum impurities: A numerically-exact tensor-network approach Matan Lotem, Frauke Schwarz, Andreas Weichselbaum, Jan Von Delft, Moshe Goldstein The accurate description of the nonequilibrium steady state properties of qubits coupled to different environments, or ``quantum impurities’’ (such as an interacting quantum dot, e.g., in the Kondo regime, under the application of a finite bias voltage) is a central open problem in condensed matter physics. In order to study such systems, we employ a novel approach where the impurity is coupled to a finite number of lead levels, which in turn are incoherently coupled to baths, resulting in a Lindblad master equation for the density operator of an effective 1D system describing the impurity and the finite leads. Numerically exact tensor-networks based methods are employed in order to target the Lindblad equation steady state. First, equilibrium NRG is used to find the relevant Hilbert subspace of the impurity and its vicinity. The full system is then evolved towards the steady state using a time dependent Matrix Product Density Operator algorithm. Our results show that the Lindblad dissipation, if appropriately tuned, can cut off the entanglement entropy growth, which otherwise is the limiting factor in tensor-networks methods, while at the same time giving rise to the correct infinite system steady state observables. |
Monday, March 2, 2020 1:03PM - 1:15PM |
B43.00008: Anomalous transport and hydrodynamics in 1D quantum systems Romain Vasseur, Utkarsh Agrawal, Sarang Gopalakrishnan, Brayden Ware In this talk, I will explain how anomalous transport can emerge in one-dimensional quantum systems at finite temperature, due to hierarchies of quasiparticle excitations. I will describe how to attack this problem using a combination of analytical (generalized hydrodynamics) and numerical (matrix product operators) techniques. |
Monday, March 2, 2020 1:15PM - 1:27PM |
B43.00009: Universal scrambling in gapless quantum spin chains Shunsuke Nakamura, Eiki Iyoda, Tetsuo Deguchi, Takahiro Sagawa Information scrambling, characterized by the out-of-time-ordered correlator (OTOC), has recently attracted much attention, because it sheds new light on chaotic dynamics on quantum many-body systems. As an important feature of OTOC, its decay rate has an upper bound, which is referred to as the chaotic bound. The scale invariance, which appears near the quantum critical region in condensed matter physics, is considered to be important for the fast decay of OTOC. |
Monday, March 2, 2020 1:27PM - 1:39PM |
B43.00010: Asymmetry in Forward/Backward Transition Times in Multi-Particle System with Interactions Jaeoh Shin, Anatoly Boris Kolomeisky Transition time is a fundamentally important property of various non-equilibrium processes, including biological transport and diffusion through channels that reflect the underlying microscopic dynamics. For single particles moving in arbitrary free-energy landscapes, it is known that the forward and backward transition times are the same due to the microscopic reversibility. To understand how and in which condition the symmetry breaks down, here we investigate a non-equilibrium one-dimensional multi-particle system on the lattice with periodic boundary conditions where the particles interact only via hard-core exclusions. We found the asymmetry in forward/backward transition times for time-averaged situations when the transition events are analyzed from long-time trajectories. We developed a fully analytical theoretical analysis that can describe the observed results. The microscopic origin of these surprising observations is discussed. |
Monday, March 2, 2020 1:39PM - 1:51PM |
B43.00011: Matrix Elements of Observables in Interacting Integrable Systems Tyler LeBlond, Krishnanand Mallayya, Lev Vidmar, Marcos Rigol We study the matrix elements of local operators in the eigenstates of an interacting integrable Hamiltonian (the spin-1/2 XXZ chain) at the center of the spectrum, and contrast their behavior with that of quantum chaotic systems. For the diagonal matrix elements, we show evidence that the support does not vanish with increasing system size, while the average eigenstate to eigenstate fluctuations vanish in a power law fashion. For the off-diagonal matrix elements, we show that their distribution is close to (but not quite) log-normal, and that their variance is a well-defined function of ω=E α −E β ({E α } are the eigenenergies) proportional to 1/D, where D is the Hilbert space dimension. |
Monday, March 2, 2020 1:51PM - 2:03PM |
B43.00012: Nonequilibrium dynamics of static electron-phonon models from Monte Carlo simulations Manuel Weber, James Freericks Electron-phonon interactions play an important role in the relaxation of strongly-correlated materials driven out of equilibrium. However, numerical simulation of microscopic models is often restricted to very small system sizes due to the unbound dimensions of the bosonic Hilbert space or requires approximative schemes (such as perturbation theory). In this talk, we present an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon models in the adiabatic limit of zero phonon frequency. We show applications to the one-dimensional Holstein and Su-Schrieffer-Heeger models and probe the formation and destruction of the ordered Peierls phase as a function of initial temperature when the system experiences strong applied electric fields. |
Monday, March 2, 2020 2:03PM - 2:15PM |
B43.00013: Heating rates in periodically driven strongly interacting quantum many-body systems Krishnanand Mallayya, Marcos Rigol We study heating rates in strongly interacting quantum lattice systems in the thermodynamic limit. Using a numerical linked cluster expansion, we calculate the energy as a function of the driving time and find a robust exponential regime. The heating rates are shown to be in excellent agreement with Fermi's golden rule. We discuss the relationship between heating rates and, within the eigenstate thermalization hypothesis, the smooth function that characterizes the off-diagonal matrix elements of the drive operator in the eigenbasis of the static Hamiltonian. We show that such a function, in nonintegrable and (remarkably) integrable Hamiltonians, can be probed experimentally by studying heating rates as functions of the drive frequency. |
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