Large-N scaling behavior of the ground-state energy and fidelity in the Dicke Model

Abstract

Within the numerically exact solution to the Dicke model proposed previously, we study the quantum criticality in terms of the ground-state (GS) energy, fidelity, and the order parameter. The finite size scaling analysis for the average fidelity susceptibility (FS) and second derivative of GS energy are performed. The correlation length exponent is obtained to be $\nu =2/3$, which is the same as that in Lipkin-Meshkov-Glick model obtained previously, suggesting the same universality. It is observed that average FS and second derivative of GS energy show similar critical behavior, demonstrating the intrinsic relation in the Dicke model. The scaling behavior for the order parameter and the singular part of the GS energy at the critical point are also analyzed and the obtained exponents are consistent with the previous scaling hypothesis in 1/N expansion scheme.

11 pages, 7 figures

References in corpus (16)

• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Quantum phase transitions of light
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Geometric phases and criticality in spin chain systems
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Ground state fidelity from tensor network representations
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Accurate numerical solution to the finite-size Dicke model
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Direct equivalence between quantum phase transition phenomena in radiation-matter and magnetic systems: scaling of entanglement
• The fidelity approach to the Hubbard model
• Scaling of Berry's Phase Close to the Dicke Quantum Phase Transition
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Scaling behavior in the adiabatic Dicke Model
• Quantum phase transition in the one-dimensional period-two and uniform compass model

Cited by in corpus (48)

• Fidelity approach to quantum phase transitions
• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Geometry of quantum phase transitions
• On the critical exponent of a quantum noise driven phase transition: the open system Dicke-model
• Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
• Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
• Quantum Phase Transition in the Sub-Ohmic Spin-Boson Model: Extended Coherent-state Approach
• Entanglement dynamics of two independent Jaynes-Cummings atoms without rotating-wave approximation
• Classical chaos in atom-field systems
• Delocalization and quantum chaos in atom-field systems
• Conventional quantum phase transition driven by complex parameter in non-Hermitian PT-symmetric Ising model
• Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate
• Criticality-enhanced quantum sensing in ferromagnetic Bose-Einstein condensates: role of readout measurement and detection noise
• Finite-size scaling analysis in the two-photon Dicke model
• Solutions to the quantum Rabi model with two equivalent qubits
• Quantum phase transitions in coupled two-level atoms in a single-mode cavity
• Generalized coherent-squeezed-state expansion for the quantum Rabi model
• Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
• Analytical description of the survival probability of coherent states in regular regimes
• Adiabatic invariants for the regular region of the Dicke model
• Quantum criticality of the Rabi-Stark model at finite frequency ratios
• Single-photon-triggered quantum chaos
• Efficient basis for the Dicke Model I: theory and convergence in energy
• Critical relaxation with overdamped quasiparticles in open quantum systems
• Probing the quantum phase transition in the Dicke model through mechanical vibrations
• Geometric phase and phase diagram for non-Hermitian quantum XY model
• Regularity and chaos in cavity QED
• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
• Dicke-type phase transition in a multimode optomechanical system
• On the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model
• Rich phase diagram of quantum phases in the anisotropic subohmic spin-boson model
• Critical exponents for an impurity in a bosonic Josephson junction: Position measurement as a phase transition
• Ground-State Fidelity and Kosterlitz-Thouless Phase Transition for Spin 1/2 Heisenberg Chain with Next-to-the-Nearest-Neighbor Interaction
• Quantum tricritical point emerging in the spin-boson model with two dissipative spins in staggered biases
• Fidelity, susceptibility and critical exponents in the Dicke model
• Ground-state properties of the two-site Hubbard-Holstein model: an exact solution
• Phase Transitions in the Anisotropic Dicke-Stark Model with $A$-square terms
• Complexity and instability of quantum motion near a quantum phase transition
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Quantum phase transition without gap opening
• Quantum criticality driven by the cavity coupling in Rabi-dimer model
• Large-N scaling behavior of the quantum fisher information in the Dicke model
• Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder
• Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm
• nuHOPS: A quantum trajectory method for highly excited environments in non-Markovian open quantum dynamics
• Berry Phase and Fidelity in the Dicke model with $A^2$ term
• Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model