Fidelity Susceptibility in the Quantum Rabi Model

Abstract

Quantum criticality usually occurs in many-body systems. Recently it was shown that the quantum Rabi model, which describes a two-level atom coupled to a single model cavity field, presents quantum phase transitions from a normal phase to a superradiate phase when the ratio between the frequency of the two level atom and the frequency of the cavity field extends to infinity. In this work, we study quantum phase transitions in the quantum Rabi model from the fidelity susceptibility perspective. We found that the fidelity susceptibility and the generalized adiabatic susceptibility present universal finite size scaling behaviors near the quantum critical point of the Rabi model if the ratio between frequency of the two level atom and frequency of the cavity field is finite. From the finite size scaling analysis of the fidelity susceptibility, we found that the adiabatic dimension of the fidelity susceptibility and the generalized adiabatic susceptibility of fourth order in the Rabi model are $4/3$ and $2$, respectively. Meanwhile the correlation length critical exponent and the dynamical critical exponent in the quantum critical point of the Rabi model are found to be $3/2$ and $1/3$ respectively. Since the fidelity susceptibility and the generalized adiabatic susceptibility are the moments of the quantum noise spectrum which is directly measurable by experiments in linear response regime, the scaling behavior of the fidelity susceptibility in the Rabi model could be tested experimentally. The simple structure of the quantum Rabi model paves the way for experimentally observing the universal scaling behavior of the fidelity susceptibility at a quantum phase transition.

arXiv comment6 pages, 6 Figures

References in corpus (36)

• Nonequilibrium dynamics of closed interacting quantum systems
• Scaling of Entanglement close to a Quantum Phase Transitions
• Ground state overlap and quantum phase transitions
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Fidelity approach to quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Quench dynamics near a quantum critical point
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Quantum Critical Scaling of Fidelity Susceptibility
• Quantum Rabi Model with Trapped Ions
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Universal scaling and critical exponents of the anisotropic quantum Rabi model
• Ground-state fidelity in one-dimensional gapless model
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Quantum Phase Transition in the Finite Jaynes-Cummings Lattice Systems
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Quantum fidelity in the thermodynamic limit
• Probing the Dynamics of Superradiant Quantum Phase Transition in a Single Trapped-Ion
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Quench dynamics near a quantum critical point: application to the sine-Gordon model
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Fidelity Between Partial States as Signature of Quantum Phase Transitions
• Exact results for fidelity susceptibility of the quantum Ising model: The interplay between parity, system size, and magnetic field
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Fidelity susceptibility of the quantum Ising model in the transverse field: The exact solution
• Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models
• Generalized fidelity susceptibility at phase transitions
• Current fidelity susceptibility and conductivity in one-dimensional lattice models with open and periodic boundary conditions
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Numerical studies of ground state fidelity of the Bose-Hubbard model
• Quantum Renormalization Group for Ground-State Fidelity

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• Critical Quantum Metrology with Fully-Connected Models: From Heisenberg to Kibble-Zurek Scaling
• Fidelity Susceptibility in One-dimensional Disordered Lattice Models
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Quantum criticality and state engineering in the simulated anisotropic quantum Rabi model
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• Fidelity as a probe for a deconfined quantum critical point
• Out-of-time-order correlators and quantum phase transitions in the Rabi and Dicke model
• Fidelity susceptibility of the anisotropic $XY$ model: The exact solution
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Quantum criticality of the Rabi-Stark model at finite frequency ratios
• Quantum fidelity susceptibility in excited state quantum phase transitions: application to the bending spectra of nonrigid molecules
• Quantum Phase Diagrams of Matter-Field Hamiltonians I: Fidelity, Bures Distance, and Entanglement
• Quantum phase transition in XXZ central spin model
• Fidelity and entanglement entropy for infinite-order phase transitions
• Linking Phase Transitions and Quantum Entanglement at Arbitrary Temperature
• Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators
• Quantum criticality driven by the cavity coupling in Rabi-dimer model
• Long-Range Order and Quantum Criticality in Antiferromagnetic Chains with Long-Range Staggered Interactions