Topological quantum phases cannot be characterized by local order parameters in the bulk. In this work, however, we show that nonanalytic signatures of a topological quantum critical point do remain in local observables in the bulk, and manifest themselves as nonanalyticities in their expectation values taken over a family of nonequilibrium states generated using a quantum quench protocol. The signature can be used for precisely locating the critical points in parameter space. A large class of initial states can be chosen for the quench, including finite temperature states. We demonstrate these results in tractable models of noninteracting fermions exhibiting topological phase transitions in one and two spatial dimensions. We also show that the nonanalyticities can be absent if the gap closing is nontopological, i.e., when it corresponds to no phase transition.
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.
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.
We reveal a prethermal dynamical regime upon suddenly quenching to the vicinity of a quantum phase transition in the time evolution of one-dimensional spin chains. The prethermal regime is analytically found to be self-similar and its duration is governed by the ground-state energy gap. Based on analytical insights and numerical evidence, we show that this dynamical regime universally exists independently of the location of the probe site, the presence of weak interactions, or the initial state. The resulting prethermal dynamics leads to an out-of-equilibrium scaling function of the order parameter in the vicinity of the transition. Our theory suggests that sudden quench dynamics, besides probing quantum phase transitions, may give rise to a universal critical slowing down near the critical point.
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.
Quantum phase transitions occur strictly at zero temperature and are accessed by varying a physical parameter such as a magnetic field or chemical potential. While these transitions themselves are experimentally inaccessible, the existence of a zero temperature quantum critical point has remarkable effects on the dynamical properties of interacting quantum many-body systems at finite temperatures. In this thesis, we study dynamics in four strongly interacting many-body systems near quantum critical points in the context of NMR relaxation, quantum quenches, many-body quantum chaos, and charge diffusion. In chapter 1, we begin by revisiting the issue of NMR relaxation in the quantum disordered phase of Ising spin chains. We find that the imaginary part of the spin susceptibility at low frequences is dominated by rare quantum processes which leads to an NMR relaxation rate that scales as
1/T1∼exp(−T2Δ) near the quantum critical point rather than the previously conjectured
1/T1∼exp(−TΔ). These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system
CoNb2O6. In chapter 2, we study the non-equilibrium dynamics of Sachdev-Ye-Kitaev (SYK) models with
q body interactions after a quantum quench, considering a quench protocol which drives the system from an initial state with long-lived quasiparticle excitations to a final state lacking any long-lived quasiparticle excitations. For
q=4, we find that the timescale for the system to locally thermalize
τeq∼kBTℏ and for
q→∞ we find that the system thermalizes instantaneously. In chapter 3, we study the real time dynamics of quantum electrodynamics in 2+1 dimensions with
Nf flavors of fermions. We focus on thermalization and the onset of many-body quantum chaos and compute the quantum Lyapunov exponent in a
Nf1 expansion. We briefly comment on chaos, locality, and gauge invariance. Finally, in Chapter 4 we consider whether the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals by computing the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength ``hydrodynamic" disorder. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.