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arXiv:2107.13916 · Physical Review A

Finite-size scaling of coherence and steered coherence in the Lipkin-Meshkov-Glick model

Ming‐Liang Hu, Fan Fang, Heng Fan

Published Dec 10, 2021• 31 citations
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Abstract

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.

DOI
10.1103/physreva.104.062416

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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.
We derive a general formula for the reduced fidelity susceptibility when the reduced density matrix is 2x2 block diagonal. By using this result and a continuous unitary transformation, we study finite-size scaling of the reduced fidelity susceptibility in the Lipkin-Meshkov-Glick model. It is found that it can well characterize quantum phase transitions, that is, we can extract information about quantum phase transitions from only the fidelity of a subsystem, which is of practical use in experiments.
We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick model by means of the Holstein-Primakoff representation of the spin operators and the continuous unitary transformations method. This combination allows us to exactly compute the leading corrections to the ground-state energy, the gap, the magnetization, and the two-spin correlation functions. We also present numerical calculations for large system size which confirm the validity of this approach. Finally, we use these results to discuss the entanglement properties of the ground state focusing on the (rescaled) concurrence that we compute in the thermodynamical limit.
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.
An analysis of the classical and quantum phase transitions of the Lipkin-Meshkov-Glick model is presented. It is shown that the classical dynamics is ruled by the energy surface of the system. Applying the catastrophe formalism to this energy surface the separatrix is obtained. It determines the regions in the control parameter space where there are phase transitions. Special attention is given to the compositions of ground and first-excited energy states, which are well described by the even and odd SU(2) coherent states. Phase transitions are shown to be associated with a change in the wave functions from collective to single-particle behavior. Evaluating the distribution of nearest-neighbor spacings it is shown that the separatrix of the system emerges as a useful tool to describe the global behavior of the quantum-level structure and their corresponding wave functions.
We report on quantum revivals and classical periodicities of wave packets centered around the ground state within the Lipkin-Meshkov-Glick model. Special attention is paid to the behavior at first- and second-order phase transitions. In line with previous studies, we find that away from criticality, characteristic times exhibit smooth, nonsingular behavior, but upon approaching the transition points they diverge as power laws with associated critical exponents. Finite-size effects are studied and the observed phenomenology is discussed in the framework of the time-energy uncertainty relation.