Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
arXiv:2107.05758 · doi:10.1103/PhysRevE.104.014113
Abstract
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.
arXiv comment16 pages, 12 figures
References in corpus (50)
- Weyl and Dirac Semimetals in Three Dimensional Solids
- Ground state overlap and quantum phase transitions
- Chaos and the Quantum Phase Transition in the Dicke Model
- Fidelity approach to quantum phase transitions
- Quantum Chaos Triggered by Precursors of a Quantum Phase Transition: The Dicke Model
- Quantum critical scaling of the geometric tensors
- Entanglement and the Phase Transition in Single Mode Superradiance
- Geometry and non-adiabatic response in quantum and classical systems
- Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
- Excited state quantum phase transitions in many-body systems
- Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
- Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
- Floquet time crystal in the Lipkin-Meshkov-Glick model
- The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
- Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
- Geometry of quantum phase transitions
- Classifying and measuring the geometry of the quantum ground state manifold
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Accurate numerical solution to the finite-size Dicke model
- Adiabatic eigenstate deformations as a sensitive probe for quantum chaos
- Quantum Fisher information as signature of superradiant quantum phase transition
- Large N Scaling Behavior of the Lipkin-Meshkov-Glick Model
- Quantum fidelity in the thermodynamic limit
- Extracting the quantum metric tensor through periodic driving
- Entanglement and Entropy in a Spin-Boson Quantum Phase Transition
- Orthogonality Catastrophe as a Consequence of the Quantum Speed Limit
- Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
- Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
- Interferometric Unruh detectors for Bose-Einstein condensates
- Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
- Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model
- Ubiquitous quantum scarring does not prevent ergodicity
- Dynamical signatures of quantum chaos and relaxation timescales in a spin-boson system
- Dynamics of the Dicke model close to the classical limit
- Information geometric methods for complexity
- Steady-state Hall response and quantum geometry of driven-dissipative lattices
- Information Geometry and Quantum Phase Transitions in the Dicke Model
- Geodesics in Information Geometry : Classical and Quantum Phase Transitions
- Probing localization and quantum geometry by spectroscopy
- Geometric Critical Exponents in Classical and Quantum Phase Transitions
- Fidelity susceptibility near topological phase transitions in quantum walks
- Quantum Information Metric and Berry Curvature from a Lagrangian Approach
- Virtues and limitations of the truncated Holstein-Primakoff description of quantum rotors
- Quantum geometric tensor and quantum phase transitions in the Lipkin-Meshkov-Glick model
- Fidelity and Uhlmann connection analysis of topological phase transitions in two dimensions
- Quantum distance and the Euler number index of the Bloch band in a 1D spin model
- Classical analog of the quantum metric tensor
- Phase space formulation of the Abelian and non-Abelian quantum geometric tensor
- Geometry of the parameter space of a quantum system: Classical point of view
- The quantum geometric tensor from generating functions
Cited by in corpus (4)
- Finite-size criticality in fully connected spin models on superconducting quantum hardware
- Quantum geometry in many-body systems with precursors of criticality
- Switchable selective interactions in a Dicke Model with Driven Biased term
- Generalized quantum geometric tensor for excited states using the path integral approach