Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
| Autor: | Daniel Gutiérrez-Ruiz, J. David Vergara, Diego Gonzalez |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Quantum phase transition
Physics Quantum Physics Statistical Mechanics (cond-mat.stat-mech) Scalar (mathematics) Classical Physics (physics.class-ph) FOS: Physical sciences Geometry Physics - Classical Physics Parameter space Metric (mathematics) Thermodynamic limit Metric tensor (general relativity) Quantum Physics (quant-ph) Quantum Condensed Matter - Statistical Mechanics Scalar curvature |
| DOI: | 10.48550/arxiv.2107.05758 |
| Popis: | We study the classical analog of the quantum metric tensor and its scalar curvature for two well-known quantum physics models. First, we analyze the geometry of the parameter space for the Dicke model with the aid of the classical and quantum metrics and find that, in the thermodynamic limit, they have the same divergent behavior near the quantum phase transition, as opposed to their corresponding scalar curvatures which are not divergent there. On the contrary, under resonance conditions, both scalar curvatures exhibit a divergence at the critical point. Second, we present the classical and quantum metrics for the Lipkin-Meshkov-Glick model in the thermodynamic limit and find a perfect agreement between them. We also show that the scalar curvature is only defined on one of the system's phases and that it approaches a negative constant value. Finally, we carry out a numerical analysis for the system's finite sizes, which clearly shows the precursors of the quantum phase transition in the metric and its scalar curvature and allows their characterization as functions of the parameters and of the system's size. Comment: 16 pages, 12 figures |
| Databáze: | OpenAIRE |
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