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arXiv:2101.04985 · Physical review. E

Work statistics and symmetry breaking in an excited-state quantum phase transition

Zakaria Mzaouali, Ricardo Puebla, John Goold, M. El Baz, Steve Campbell

Published Mar 25, 2021• 23 citations
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Abstract

We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.

DOI
10.1103/physreve.103.032145

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We examine how the presence of an excited-state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited-state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.
We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the groundstate and by employing the Loschmidt echo, we see manifestly different dynamics are present if the system is quenched through the critical point. Furthermore, we show that the average work shows no sensitivity to the quantum phase transition, however the free energy and irreversible work show markedly different rates of change in each phase. Finally, we assess the spectral function showing the fundamental excitations that dictate the dynamics of the post-quenched system, further highlighting the qualitative differences between the dynamics in the two phases.
We examine the dynamics after a sudden quench in the magnetic field of the Lipkin-Meshkov-Glick model. Starting from the ground state and by employing the time-dependent fidelity, we see manifestly different dynamics are present if the system is quenched through the critical point. Furthermore, we show that the average work shows no sensitivity to the quantum phase transition; however, the free energy and irreversible work show markedly different rates of change in each phase. Finally, we assess the spectral function showing the fundamental excitations that dictate the dynamics of the postquenched system, further highlighting the qualitative differences between the dynamics in the two phases.
Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.
Using the diagonal entropy, we analyze the dynamical signatures of the Lipkin-Meshkov-Glick model excited-state quantum phase transition (ESQPT). We first show that the time evolution of the diagonal entropy behaves as an efficient indicator of the presence of an ESQPT. We also compute the probability distribution of the diagonal entropy values over a certain time interval and we find that the resulting distribution provides a clear distinction between the different phases of ESQPT. Moreover, we observe that the probability distribution of the diagonal entropy at the ESQPT critical point has a universal form, well described by a beta distribution, and that a reliable detection of the ESQPT can be obtained from the diagonal entropy central moments.
Studying the implications and characterizations of the excited-state quantum phase transitions (ESQPTs) would enable us to understand various phenomena observed in quantum many-body systems. In this work, we delve into the affects and characterizations of the ESQPTs in the anharmonic Lipkin-Meshkov-Glick (LMG) model by means of the entropy of the quantum work distribution. The entropy of the work distribution measures the complexity of the work distribution and behaves as a valuable tool for analyzing nonequilibrium work statistics. We show that the entropy of the work distribution captures salient signatures of the underlying ESQPTs in the model. In particular, a detailed analysis of the scaling behavior of the entropy verifies that it not only acts as a witness of the ESQPTs but also reveals the difference between different types of ESQPTs. We further demonstrate that the work distribution entropy also behaves as a powerful tool for understanding the features and differences of ESQPTs in the energy space. Our results provide further evidence of the usefulness of the entropy of the work distribution for investigating various phase transitions in quantum many-body systems and open up a promising way for experimentally exploring the signatures of ESQPTs.
Excited-state quantum phase transitions extend the quantum phase transition concept beyond the ground state and offer insights into the complex behavior of quantum systems. In the present work we assess the use of the multiple quantum coherence spectrum as a valid tool to probe excited-state quantum phase transitions within the framework of the Lipkin-Meshkov-Glick model. The time dependence and the long-time average of the multiple quantum coherence spectrum reveal the intricate dynamics that stems from the existence of singularities in the excited-state spectrum of a quantum many-body system.