期刊
PHYSICAL REVIEW B
卷 103, 期 17, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.103.174104
关键词
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资金
- Computation Center-ICN
- CONACyT [332577]
- DGAPA-UNAM postdoctoral fellowship
- Consejo Nacional de Ciencia y Tecnologia (CONACyT), Mexico [A1-S-7701]
- DGAPAPAPIIT [IN103919, IN104020]
This study investigates the quantum metric tensor and scalar curvature of a specific version of the Lipkin-Meshkov-Glick model, analyzing ground-state and excited-state quantum phase transitions. By utilizing the Holstein-Primakoff approximation, analytic expressions for quantum metric tensor and curvatures were derived and compared with finite-size numerical results, showing good agreement except near phase transition points. The classical Hamiltonian was constructed using Bloch coherent states, revealing stability changes and bifurcation during quantum phase transitions.
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 in 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 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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