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arXiv:2012.15501 · Physical review. B./Physical review. B

Universal scaling of work statistics in conformal field theory models

Zhaoyu Fei, C. P. Sun

Published Apr 27, 2021• 4 citations
arXivHTMLPDF

Abstract

We systematically study the work statistics for quantum phase transition. For a quantum system approached by an anisotropic conformal field theory near the critical point, the driving protocol is divided into three different regimes for different quench rates, which reflects the competition between the frozen time and the quench timescale. In each regime, we find universal scaling behaviors in work statistics (after renormalization). It is shown that the critical exponents are determined by the space-time dimension $d$, the dynamical critical exponent $z$, the correlation-length exponent $\ensuremath{\nu}$, and the power-law protocols. These universal scalings in nonequilibrium processes may be found in quantum phase transition by measuring the Loschmidt echo or the Ramsey interferometry.

DOI
10.1103/physrevb.103.144204

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We systematically study the work statistics for quantum phase transition. For a quantum system approached by an anisotropic conformal field theory near the critical point, the driving protocol is divided into three different regimes for different quench rates, which reflects the competition between the frozen time and the quench timescale. In each regime, we find universal scaling behaviors in work statistics (after renormalization). It is shown that the critical exponents are determined by the space-time dimension ddd, the dynamical critical exponent zzz, the correlation-length exponent \ensuremathν\ensuremath{\nu}\ensuremathν, and the power-law protocols. These universal scalings in nonequilibrium processes may be found in quantum phase transition by measuring the Loschmidt echo or the Ramsey interferometry.
We investigate the statistics of the work performed during a quench across a quantum phase transition using the adiabatic perturbation theory when the system is characterized by independent quasiparticles and the "single-excitation" approximation is assumed. It is shown that all the cumulants of work exhibit universal scaling behavior analogous to the Kibble-Zurek scaling for the average density of defects. Two kinds of transformations are considered: quenches between two gapped phases in which a critical point is traversed, and quenches that end near the critical point. In contrast to the scaling behavior of the density of defects, the scaling behavior of the cumulants of work are shown to be qualitatively different for these two kinds of quenches. However, in both cases the corresponding exponents are fully determined by the dimension of the system and the critical exponents of the transition, as in the traditional Kibble-Zurek mechanism (KZM). Thus, our study deepens our understanding about the nonequilibrium dynamics of a quantum phase transition by revealing the imprint of the KZM on the work statistics.
Measuring universal data in the strongly correlated regime of quantum critical points remains a fundamental objective for quantum simulators. In foundational work, Calabrese and Cardy demonstrated how these data govern the dynamics of certain global quenches to 1+1-dimensional conformal field theories. While the quasiparticle picture they introduce has been widely successful in both theory and experiment, their seminal prediction that the critical exponents are simply encoded in the relaxation rates of local observables is challenging to investigate experimentally. In this Letter, we examine the critical quench dynamics of local observables from two types of readily accessible initial conditions: ground states and finite-temperature ensembles. We identify universal scaling collapses and scaling functions, utilizing a combination of conformal perturbation theory and tensor network numerics. For the finite-temperature quenches, we determine a regime in which the conformal field theory results are recovered, thereby allowing universal quantum critical data to be extracted from realistic quenches.
A quantum critical system described at low energy by a conformal field theory (CFT) and subjected to a time-periodic boundary drive displays multiple dynamical regimes, depending on the drive frequency. We compute the behavior of quantities including the entanglement entropy and Loschmidt echo, confirming analytic predictions from field theory by exact numerics on the transverse field Ising model and demonstrate universality by adding nonintegrable perturbations. The dynamics naturally separate into three regimes: a slow-driving limit, which has an interpretation as multiple quantum quenches with amplitude corrections from CFT; a fast-driving limit, in which the system behaves as though subject to a single quantum quench; and a crossover regime displaying heating. The universal Floquet dynamics in all regimes can be understood using a combination of boundary CFT and Kibble-Zurek scaling arguments.
Dynamical quantum phase transitions (DQPTs) at critical times appear as nonanalyticities during nonequilibrium quantum real-time evolution. Although there is evidence for a close relationship between DQPTs and equilibrium phase transitions, a major challenge is still to connect to fundamental concepts such as scaling and universality. In this work, renormalization group transformations in complex parameter space are formulated for quantum quenches in Ising models showing that the DQPTs are critical points associated with unstable fixed points of equilibrium Ising models. Therefore, these DQPTs obey scaling and universality. On the basis of numerical simulations, signatures of these DQPTs in the dynamical buildup of spin correlations are found with an associated power-law scaling determined solely by the fixed point's universality class. An outlook is given on how to explore this dynamical scaling experimentally in systems of trapped ions.
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