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arXiv:2209.02510 · Physical Review A

Characterizing the Lipkin-Meshkov-Glick excited-state spectrum through the quantum coherence spectrum

Qian Wang, Jamil Khalouf-Rivera, Francisco Pérez-Bernal

Published Mar 11, 2025• 2 citations
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Abstract

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.

DOI
10.1103/physreva.111.032209

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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.
We propose a new method to characterize equilibrium quantum phase transitions in terms of the spectrum of multiple quantum coherence (MQC) intensities, a special type of out-of-time-order correlation. Using the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as illustrative examples, we show that an abrupt change in coherence and entanglement of the ground state across a quantum phase transition is clearly observable in the MQC spectrum. Furthermore, we develop a robust protocol to obtain the MQC intensities across the ground state phase diagram, which is accessible to a broad range of current experiments as it relies on standard quasi-adiabatic quenches without the requirement of time-reversing the dynamics.
We investigate signatures of the excited-state quantum phase transition in the periodic dynamics of the Lipkin-Meshkov-Glick model. With this aim, we use the semiclassical trajectories to calculate quantum mechanical quantities such as the density of states and expectation values of observables in eigenstates of the system. Motivated by this approach, we suggest an experimental protocol, based on the time evolution of the finite-size system, to find singularities in observables, which arise due to the excited-state quantum phase transition. We also discuss the influence of the participation ratio on the deviations of the quantum mechanical finite-size time evolution from the classical one.
Using the Husimi quasiprobability distribution, we investigate the phase space signatures of excited-state quantum phase transitions (ESQPTs) in the Lipkin-Meshkov-Glick and coupled top models. We show that the ESQPT is evinced by the dynamics of the Husimi function, that exhibits a distinct time dependence in the different ESQPT phases. We also discuss how to identify the ESQPT signatures from the long-time averaged Husimi function and its associated marginal distributions. Moreover, from the calculated second moment and Wherl entropy of the long-time averaged Husimi function, we estimate the critical points of the ESQPT in both models, obtaining a good agreement with analytical (mean field) results. We provide a firm evidence that phase space methods are both a new probe for the detection and a valuable tool for the study of ESQPTs.
Quantum coherence reflects the origin of quantumness and might be capable of extracting the subtle nature of a system. We investigate the ground-state coherence and steered coherence in the Lipkin-Meshkov-Glick model and show that they detect faithfully the quantum phase transitions of this model. Moreover, we carry out scaling analysis on the coherence and steered coherence by means of the continuous unitary transformation method and find that the scaling exponents are uniquely determined by the phase region of this model. These results may provide useful insights into the mechanism underlying quantum criticality in many-body systems.