Geodesics in Information Geometry : Classical and Quantum Phase Transitions

Abstract

We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase transitions, in the thermodynamic limit. It is established that both in the classical as well as in the quantum case, geodesics are confined to a single phase, and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.

1 + 12 pages, 4 .eps figures

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• Geometry of the parameter space of a quantum system: Classical point of view
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• Topology of restricted phase space thermodynamics in Kerr-Sen-Ads black holes
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• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
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• Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Search for optimal driving in finite quantum systems with precursors of criticality
• Quantum geometry in many-body systems with precursors of criticality
• Generalized quantum geometric tensor for excited states using the path integral approach
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• Conventional vs. modified GTD metrics: Survival of modified GTD metrics in AdS spacetime and thermodynamic ensembles