In recent times it has been observed that signatures of equilibrium quantum criticality surprisingly show up in many-body systems, which are manifestly far from equilibrium. We explore such scenarios in interacting spin systems subject to a quench and develop a robust method to systematically probe ground-state critical physics through nonequilibrium post-quench dynamics. Analyzing late-time behavior of finite string-like observables, we find emerging sharp signatures of equilibrium criticality. Specifically, these observables accurately detect equilibrium critical points and universal scaling exponents after long times following a quench. This happens despite the fact that the analyzed systems are strongly chaotic/ergodic and is interestingly due to a strong memory of the initial conditions retained by these observables after quench. We find that our results can also be used to explain critical signatures in post-quench domain formation, seen in a recent experiment with trapped ion quantum simulators.
In recent times it has been observed that signatures of equilibrium quantum criticality surprisingly show up in many-body systems, which are manifestly far from equilibrium. We explore such scenarios in interacting spin systems subject to a quench and develop a robust method to systematically probe ground-state critical physics through nonequilibrium post-quench dynamics. Analyzing late-time behavior of finite string-like observables, we find emerging sharp signatures of equilibrium criticality. Specifically, these observables accurately detect equilibrium critical points and universal scaling exponents after long times following a quench. This happens despite the fact that the analyzed systems are strongly chaotic/ergodic and is interestingly due to a strong memory of the initial conditions retained by these observables after quench. We find that our results can also be used to explain critical signatures in post-quench domain formation, seen in a recent experiment with trapped ion quantum simulators.
Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e. a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.
Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground-state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model describing the collective interaction of N spins and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the postquench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely nonequilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as N^{1/3}), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the nonequilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
Extracting critical behavior in the wake of quantum quenches has recently been at the forefront of theoretical and experimental investigations in condensed matter physics and quantum synthetic matter, with particular emphasis on experimental feasibility. Here, we investigate the potential of single-site observables in probing equilibrium phase transitions and dynamical criticality in short-range transverse-field Ising chains. For integrable and near-integrable models, our exact and mean-field-theory analyses reveal a truly out-of-equilibrium universal scaling exponent in the vicinity of the transition that is independent of the initial state and the location of the probe site so long as the latter is sufficiently close to the edge of the chain. Signature of a dynamical crossover survives when integrability is strongly broken. Our work provides a robust scheme for the experimental detection of quantum critical points and dynamical scaling laws in short-range interacting models using modern ultracold-atom setups.
Quantum phase transitions are highly remarkable phenomena manifesting in quantum many-body systems. However, their precise identifications in equilibrium systems pose significant theoretical and experimental challenges. Thus far, dynamical detection protocols employing global quantum quenches have been proposed, wherein transitions are discerned via global nonequilibrium excitations. In this work, we demonstrate that quantum phase transitions can be detected through localized out-of-equilibrium excitations induced by local quantum quenches. While the resulting dynamics after the quench is influenced by both the local quench operation and the intrinsic dynamics of the quantum system, the effects of the former are exclusively extracted using the cutting-edge framework called quantum reservoir probing (QRP). Through the QRP, we find that the impacts of the local quenches vary across different quantum phases and are significantly suppressed by quantum fluctuations amplified near quantum critical points; consequently, phase boundaries are precisely delineated. We demonstrate that the QRP can detect quantum phase transitions in the paradigmatic integrable and nonintegrable quantum spin systems, and even topological quantum phase transitions, all within the identical framework employing local quantum quenches and single-site observables. Quantum phase transitions, traditionally examined for divergent fluctuations in space and time at equilibrium, are now revealing local, nonequilibrium signatures. Kobayashi and Motome explore nonequilibrium quantum dynamics triggered by local quantum quenches utilizing a new approach of quantum reservoir probing.
Quantum phase transitions are central to our understanding of why matter at very low temperatures can exhibit starkly different properties upon small changes of microscopic parameters.Accurately locating those transitions is challenging experimentally and theoretically.Here, we show that the antithetic strategy of forcing systems out of equilibrium via sudden quenches provides a route to locate quantum phase transitions.Specifically, we show that such transitions imprint distinctive features in the intermediate-time dynamics, and results after equilibration, of local observables in quantum chaotic spin chains.Furthermore, we show that the effective temperature in the expected thermal-like states after equilibration can exhibit minima in the vicinity of the quantum critical points.We discuss how to test our results in experiments with Rydberg atoms and explore nonequilibrium signatures of quantum critical points in models with topological transitions.