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arXiv:2010.07307 · Physical review. B./Physical review. B

Local measures of dynamical quantum phase transitions

Jad C. Halimeh, Daniele Trapin, Maarten Van Damme, Markus Heyl

Published Aug 17, 2021• 48 citations
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Abstract

The authors introduce two types of local effective free energies to detect dynamical quantum phase transitions, which are a useful concept to classify nonequilibrium states of quantum matter. These local effective free energies can be employed in position or momentum space, making them ideal for various measurement techniques in modern quantum simulation platforms. The local effective free energies also allow extraction of truly out-of-equilibrium critical exponents, giving a glimpse into possible out-of-equilibrium quantum universality classes.

DOI
10.1103/physrevb.104.075130

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•May 11, 2018•0 citations
The authors introduce two types of local effective free energies to detect dynamical quantum phase transitions, which are a useful concept to classify nonequilibrium states of quantum matter. These local effective free energies can be employed in position or momentum space, making them ideal for various measurement techniques in modern quantum simulation platforms. The local effective free energies also allow extraction of truly out-of-equilibrium critical exponents, giving a glimpse into possible out-of-equilibrium quantum universality classes.
Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook to major open questions as well as future directions of research.
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.
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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In recent years, various notions of dynamical phase transitions have emerged to describe far-from-equilibrium criticality. A unifying framework connecting these different concepts is still missing, and would provide significant progress toward understanding far-from-equilibrium quantum many-body universality. Initializing our system in a thermal ensemble and subsequently performing quantum quenches in the Lipkin-Meshkov-Glick model, we establish a direct connection between excited-state quantum phase transitions (ESQPTs) and two major types of dynamical phase transitions (DPTs), by relating the phases of the latter to the critical energies and conservation laws in the former. Our work provides further insight into how various concepts of non-ground-state criticality are intimately connected, paving the way for a unified framework of far-from-equilibrium universality. Published by the American Physical Society 2024
This dissertation is devoted to the study of universal observables in quantum critical systems, most of which have a non-local character. The overarching goal of this work is to compute new universal observables of critical points to aid theoretical understanding of these systems.\nWe first consider the finite-size energy spectrum of quantum critical points on the torus. We compute the spectrum for the Wilson-Fisher conformal field theory in the epsilon=3−d\\epsilon = 3 - depsilon=3−d expansion, where the energy spectrum maps onto a strongly-coupled problem in quantum mechanics. We also compute the energy spectrum to leading order in 1/N1/N1/N, and we compare the two expansions. We then study the torus spectra associated with a class of confinement transitions in states with mathbbZ2\\mathbb{Z}_2mathbbZ2​ topological order. After introducing these universality classes, we show that the critical torus spectrum can be used to detect nontrivial effects like spontaneous symmetry breaking and emergent gauge degrees of freedom. We compare our analytic results with numerical simulations where available, demonstrating the utility of the torus spectrum as a useful characterization of the universality class of a quantum critical point.\nWe then present a computation of the von Neumann entanglement entropy of the Wilson-Fisher and Gross-Neveu conformal field theories in the large NNN limit. We obtain an exact mapping to the von Neumann entanglement entropy of a free quantum field theory, allowing an exact determination of the entanglement entropy in a number of cases. \nWe also study a critical point displaying impurity-driven critical behavior in a boson superfluid-insulator phase transition. The presence of an impurity drives the system to a new interacting universality class, which has critical exponents associated with the scaling dimensions of the impurity degree of freedom. We present the universal quantum field theory of this transition and compute the critical exponents and finite-temperature compressibility at the critical point using the epsilon\\epsilonepsilon expansion.