Information Geometry and Quantum Phase Transitions in the Dicke Model

Abstract

We study information geometry of the Dicke model, in the thermodynamic limit. The scalar curvature $R$ of the Riemannian metric tensor induced on the parameter space of the model is calculated. We analyze this both with and without the rotating wave approximation, and show that the parameter manifold is smooth even at the phase transition, and that the scalar curvature is continuous across the phase boundary.

References and clarifications added. Final version to appear in Physical Review E

References in corpus (8)

• Quantum critical scaling of the geometric tensors
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Finite-temperature mutual information in a simple phase transition
• Oscillating fidelity susceptibility near a quantum multicritical point
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model
• Information Geometry, Phase Transitions, and Widom Lines : Magnetic and Liquid Systems

Cited by in corpus (30)

• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Geometry of quantum phase transitions
• Classifying and measuring the geometry of the quantum ground state manifold
• Extracting the quantum metric tensor through periodic driving
• Information geometric methods for complexity
• Steady-state Hall response and quantum geometry of driven-dissipative lattices
• Geometric Critical Exponents in Classical and Quantum Phase Transitions
• Phase Transition in the periodically pulsed Dicke Model
• Revealing Chern number from quantum metric
• Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
• Complexity and information geometry in spin chains
• Information geometry for Fermi-Dirac and Bose-Einstein quantum statistics
• Thermodynamic Geometry of Black Holes in the Canonical Ensemble
• Exploring chaos in Dicke Model using ground state fidelity and Loschmidt echo
• Complexity in the Lipkin-Meshkov-Glick Model
• Extracting non-Abelian quantum metric tensor and its related Chern numbers
• Complexity, Information Geometry, and Loschmidt Echo near Quantum Criticality
• Connecting geometry and performance of two-qubit parameterized quantum circuits
• Identifying non-Hermitian critical points with quantum metric
• Geometry and speed of evolution for a spin-s system with long-range zz-type Ising interaction
• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Quantum geometry in many-body systems with precursors of criticality
• Information geometry and synchronization phase transition in Kuramoto model
• Time-dependent quantum geometric tensor and some applications
• Quantum geometrical effects in non-Hermitian systems
• Effect of fast scale factor fluctuations on cosmological evolution
• Single-Bubble Sonoluminescence as Dicke Superradiance at Finite Temperature
• Information geometry and Bose-Einstein condensation