Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session V44: Periodically Driven Systems and Quantum SimulationLive
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Sponsoring Units: DCMP Chair: Vadim Oganesyan, The Graduate Center, City University of New York |
Thursday, March 18, 2021 3:00PM - 3:12PM Live |
V44.00001: Geometry and black holes in periodically driven critical quantum systems Bastien Lapierre, Kenny Jing Hui Choo, Per Moosavi, Apoorv Tiwari, Clément Tauber, Titus Neupert, Ramasubramanian Chitra While driven interacting quantum matter is generically subject to heating and scrambling, certain classes of systems evade this paradigm. In this talk I will discuss such an exceptional class in periodically driven critical (1+1)-dimensional systems with a spatially modulated time-evolution operator described by a conformal field theory (CFT). I will show that such Floquet drives display both heating and non-heating phases, and that the heating phase can be interpreted as dynamical propagation of excitations through a curved space-time obtained by two black hole horizons, resulting in a singular concentration of energy at their center. Finally, I will present a new geometric approach to study generic inhomogeneous Floquet drives, generalising previous results that used only the finite-dimensional sl(2) algebra to systems that require the full use of the infinite-dimensional Virasoro algebra, exhibiting a richer phase diagram structure. |
Thursday, March 18, 2021 3:12PM - 3:24PM Live |
V44.00002: Floquet prethermalization and Rabi oscillations in optically excited Hubbard clusters Junichi Okamoto, Francesco Peronaci Floquet engineering is a growing field of study to realize exotic many-body quantum states beyond the realm of equilibrium material science. The Floquet picture in terms of effective Hamiltonians is stable in the limit of high-frequency driving, where the heating rate is suppressed. In contrast, when the driving frequency is comparable to the energies of the system, the effect of heating is non-negligible, and the analysis becomes intricate. However, even in this case, the existence of quasi-steady states, so-called Floquet prethermal states (FPSs), have been demonstrated, which expands the boundary of Floquet engineering to a realistic driving range. In this work, we have investigated the optically excited Hubbard clusters by exact diagonalization. We show that FPSs emerge not only off resonance but also for resonant excitation, provided a small field amplitude. Notably, FPSs at resonance occur with Rabi oscillations. At stronger fields, thermalization to infinite temperature is observed. We elucidate the origin of the FPSs using time-dependent perturbation theory and the two-site Hubbard model. |
Thursday, March 18, 2021 3:24PM - 3:36PM Live |
V44.00003: Introduction to the Influence matrix approach to many-body Floquet Dynamics Michael Sonner, Alessio Lerose, Dmitry Abanin In this work, we introduce an approach to study quantum many-body dynamics, inspired by the Feynman-Vernon influence functional. Focusing on a family of interacting, Floquet spin chains, we consider a Keldysh path-integral description of the dynamics. The central object in our approach is the influence matrix (IM), which describes the effect of the system on the dynamics of a local subsystem. For translationally invariant models, we formulate a self-consistency equation for the influence matrix. For certain special values of the model parameters, we obtain an exact solution which represents a perfect dephaser (PD). Physically, a PD corresponds to a many-body system that acts as a perfectly Markovian bath on itself: at each period, it measures every spin. For the models considered here, we establish that PD points include dual-unitary circuits investigated in recent works. In the vicinity of PD points, the system is not perfectly Markovian, but rather acts as a bath with a short memory time. In this case, we demonstrate that the self-consistency equation can be solved using matrix-product states (MPS) methods, as the IM temporal entanglement is low. |
Thursday, March 18, 2021 3:36PM - 3:48PM Live |
V44.00004: Thermalization dynamics in many-body Floquet dynamics via the influence matrix approach Alessio Lerose, Michael Sonner, Dmitry Abanin The influence matrix approach to quantum many-body dynamics aims at describing the effect of a system on the non-equilibrium evolution of a local subsystem. Using a combination of analytical insights and matrix-product states computations, we characterize the structure of the influence matrix in terms of an effective “statistical-mechanics” description for interfering intervals of local quantum trajectories. We illustrate the predictive power of this description by analytically computing how quickly an embedded impurity spin thermalizes. The approach formulated here provides an intuitive view of the quantum many-body dynamics problem, allows to construct models of thermalizing dynamics that are solvable or can be efficiently treated by tensor-network methods, and to further characterize quantum ergodicity or lack thereof. |
Thursday, March 18, 2021 3:48PM - 4:00PM Live |
V44.00005: Statistical Floquet prethermalization of the Bose-Hubbard model Emanuele Dalla Torre The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large frequencies. In particular, for quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, the exponential suppression of heating has also been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we develop a semiclassical description of Floquet prethermal states and link the suppressed heating rate to the low probability of finding many particles on a single site. We derive an analytic expression for the exponential suppression of heating valid at strong interactions and large temperatures, which matches the exact numerical solution of the model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems. |
Thursday, March 18, 2021 4:00PM - 4:12PM Live |
V44.00006: 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 (arguably prethermal) 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 continuous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions. |
Thursday, March 18, 2021 4:12PM - 4:24PM Live |
V44.00007: Entanglement negativity at the critical point of measurement-driven transition Bowen Shi, Xin Dai, Yuan-Ming Lu We study the entanglement behavior of a random unitary circuit punctuated by projective measurements at the measurement-driven phase transition in one spatial dimension. We numerically study the logarithmic entanglement negativity of two disjoint intervals and find that it scales as a power of the cross-ratio. We investigate two systems: (1) Clifford circuits with projective measurements, and (2) Haar random local unitary circuit with projective measurements. Previous results of entanglement entropy and mutual information point to an emergent conformal invariance of the measurement-induced transition. Remarkably, we identify a power-law behavior of entanglement negativity at the critical point, suggesting that the critical behavior of the measurement-induced transition cannot be described by any unitary conformal field theory. |
Thursday, March 18, 2021 4:24PM - 4:36PM Live |
V44.00008: Measurement induced phase transition in a solvable all-to-all Brownian circuit model Subhayan Sahu, Gregory Bentsen, Brian Swingle Competition between unitary scrambling dynamics that protects quantum information non-locally and local measurements that probe and collapse the quantum state can result in a measurement induced entanglement phase transition. Here we study this phenomenon in an all-to-all Brownian hybrid circuit model of qubits that is analytically tractable at large N. A part of the system is initially entangled with a reference which remains mixed at low measurement rates but is purified at high measurement rates. After circuit averaging, purity of the reference can be represented as a path integral coupling four replicas with twisted boundary conditions. Saddle point analysis reveals a second-order bulk phase transition corresponding to permutation symmetry breaking below a critical measurement rate. We demonstrate that this bulk transition is directly responsible for the purity transition and check our analytical results against exact diagonalization numerics. This model allows us to explicitly observe and characterize the transition without relying on numerics or the limit of large local Hilbert space dimension which were crucial in previous analytical studies. |
Thursday, March 18, 2021 4:36PM - 4:48PM Not Participating |
V44.00009: Non-equilibrium steady state solutions of time-periodic driven Luttinger liquids Serena Fazzini, Piotr Chudzinski, Christoph Dauer, Imke Schneider, Sebastian Eggert Controlled time-periodic driving of quantum systems has recently provided a whole range of possibilities for Floquet steady states with quantum engineered properties. In order to study the interplay of many-body correlations with time-periodic driving we now consider a Tomonaga-Luttinger liquid with periodically changing interactions in the steady state, which is proposed to be realized by an interacting Bose gas confined to a one-dimensional Lieb-Liniger model. Without assuming any high-frequency approximation, we are able to analyse the time-dependent Schrödinger equation by developing a Floquet-Bogliubov ansatz, which is solved in terms of Mathieu functions. Remarkably, the characteristic Mathieu exponent can also become complex valued in regions of frequency and momentum space, which does not correspond to a steady state solution. For the experimental systems this implies an instability when multiples of driving frequency approximately matches twice the dispersion energy, which is observable by the creation of a large number of collective density wave excitations at the corresponding wave numbers. |
Thursday, March 18, 2021 4:48PM - 5:00PM Live |
V44.00010: Characterizations of prethermal states in periodically driven many-body systems with unbounded chaotic diffusion Atanu Rajak, Itzhack Dana, Emanuele Dalla Torre We introduce well-defined characterizations of prethermal states in realistic periodically driven many-body systems with unbounded chaotic diffusion of the kinetic energy. These systems, interacting arrays of periodically kicked rotors, are paradigmatic models of many-body chaos theory. We show that the prethermal states in these systems are well described by a generalized Gibbs ensemble based essentially on the average Hamiltonian. The latter is the quasiconserved quantity in the prethermal state and the ensemble is characterized by the temperature |
Thursday, March 18, 2021 5:00PM - 5:12PM Live |
V44.00011: Dynamical signatures of Floquet topological phases in quantum computing Kaixiang Su, Po-Wei Lo, Michael Lawler Many body phenomena far from equilibrium present challenges beyond reach by classical computational resources, while digital quantum computers provide a possible way out. Among the intriguing aspects of dynamical many body systems, Floquet phases of matter is an especially rich area for both theoretical and experimental investigations. We propose a scheme to simulate and characterize the many body Floquet systems on a near-term quantum computer. By using a periodic circuit construction, we can then simulate the evolution of a many-body localized Floquet system exhibiting four different phases. We also define a dynamical order parameter for each phases, which can be probed using random measurements. Through numerical simulation we demonstrate that our methods can help distinguish between different Floquet phases. Moreover, our scheme can be properly adjusted to probe new many-body localized Floquet phases with unknown order parameters. Our results can be readily applied to near-term quantum computers such as IBM-Q. |
Thursday, March 18, 2021 5:12PM - 5:24PM Live |
V44.00012: Experimental Realization of Spin Liquids in a Programmable Quantum Device Shiyu Zhou, Dmitry Green, Edward Dahl, Claudio Chamon The advent of widely available computing power has spawned a whole research field that we now call computational physics. Today, we may be on the cusp of a similar paradigm shift as programmable qubit devices enable one to run experiments on a platform of actual physical quantum states. Here we use the commercially available D-Wave DW-2000Q device to build and probe a state of matter that has not been observed or fabricated before. The topological phase that we build has been widely sought for many years and is a candidate platform for quantum computation. While we cannot observe the full quantum regime due to the limitations of the current device, we do observe unmistakable signatures of the phase in its classical limit at the endpoint of the quantum annealing protocol. In the process of doing so, we identify additional features that a programmable device of this sort would need in order to implement fully functional topological qubits. It is a testament to technological progress that a handful of theorists can observe and experiment with new physics while being equipped only with remote access to a commercial device. |
Thursday, March 18, 2021 5:24PM - 5:36PM Live |
V44.00013: Self-Organized Error Correction in Random Unitary Circuits with Measurement Ruihua Fan, Sagar Vijay, Ashvin Vishwanath, Yizhuang You Random measurements have been shown to induce a phase transition in 1D quantum system evolving under chaotic local unitary dynamics. In this talk, we will the subthermal volume law phase and its connection to quantum error-correcting codes. We study the mutual information between a qudit inside a region and the exterior and identifying a power law decay with distance from the region's boundary with power 3/2. It implies that measurement deep inside the region will have negligible effect on its entanglement. We also find a universal, subleading logarithmic contribution to the volume law entanglement entropy, which is intimately related to the first observation in our formalism. Finally, we adopt the quantum Hamming bound to obtain a bound on the critical measurement strength as a function of the qudit dimension. The bound is saturated at infintie qudit dimension and provides a reasonable estimate for the qubit transition. |
Thursday, March 18, 2021 5:36PM - 5:48PM Live |
V44.00014: Spin Squeezing as a Probe of Quantum Materials Ilija Nikolov, Adrian G Del Maestro, Chandrasekhar Ramanathan, Vesna Mitrovic A nuclear spin squeezed state describes the quantum state of the collective spin for which the variance of one of the spin angular momentum components is below the Standard Quantum Limit. Spin squeezing techniques can be naturally implemented in systems with interacting and/or entangled spin ensembles. We present a novel Nuclear Magnetic Resonance (NMR) method based on using nuclear spin squeezed states to locally probe emergent orders in quantum materials (e.g. orbital order). |
Thursday, March 18, 2021 5:48PM - 6:00PM Live |
V44.00015: Non-unitary dynamics in N-qubit quantum circuits and its link with complex temperature statistical mechanics of the Ising Model Sankhya Basu, Sarang Gopalakrishnan, Vadim Oganesyan, Christopher A Hooley This talk primarily focuses on the relationship between non-unitary dynamics of a N-qubit quantum circuits with measurement and the spin-spin correlations of the N-leg Ising ladder at complex temperatures. In the large N-limit of the Ising ladder, we will show that there is a finite region in the complex fugacity plane in which spin-spin correlations exhibit incommensurate oscillatory (quasi)long range correlations. We argue that these are due to 'partial unitarity' of an associated N-qubit quantum circuit, whereby some coherence is retained in the long time limit. We also show that there exists special points in the complex fugacity plane where full unitarity is recovered. |
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