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arXiv · 2105.11551

Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model

Daniel Gutiérrez-Ruiz·Diego Gonzalez·Jorge Chávez-Carlos·Jorge G. Hirsch·J. David Vergara
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Abstract

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs, showing a change of stability associated with an excited state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state. Employing the Holstein-Primakoff approximation, we derive analytic expressions for the quantum metric tensor and compute the scalar and Berry curvatures. We contrast the analytic results with their finite-size counterparts obtained through exact numerical diagonalization and find an excellent agreement between them for large sizes of the system in a wide region of the parameter space, except in points near the phase transition where the Holstein-Primakoff approximation ceases to be valid.

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Daniel Gutiérrez-Ruiz, Diego Gonzalez, Jorge Chávez-Carlos, Jorge G. Hirsch, J. David Vergara. 2021-05-24. Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model. https://doi.org/10.1103/physrevb.103.174104

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