Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
| Autor: | Jorge G. Hirsch, Diego Gonzalez, Jorge Chávez-Carlos, J. David Vergara, Daniel Gutiérrez-Ruiz |
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| Rok vydání: | 2021 |
| Předmět: |
Quantum phase transition
Physics Phase transition Quantum Physics Scalar (physics) FOS: Physical sciences 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Condensed Matter - Other Condensed Matter symbols.namesake 0103 physical sciences symbols Coherent states Tensor Metric tensor (general relativity) 010306 general physics 0210 nano-technology Hamiltonian (quantum mechanics) Quantum Physics (quant-ph) Scalar curvature Mathematical physics Other Condensed Matter (cond-mat.other) |
| DOI: | 10.48550/arxiv.2105.11551 |
| Popis: | 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. Comment: 14 pages |
| Databáze: | OpenAIRE |
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