Scaling dimension of fidelity susceptibility in quantum phase transitions

Abstract

We analyze ground-state behaviors of fidelity susceptibility (FS) and show that the FS has its own distinct dimension instead of real system's dimension in general quantum phases. The scaling relation of the FS in quantum phase transitions (QPTs) is then established on more general grounds. Depending on whether the FS's dimensions of two neighboring quantum phases are the same or not, we are able to classify QPTs into two distinct types. For the latter type, the change in the FS's dimension is a characteristic that separates two phases. As a non-trivial application to the Kitaev honeycomb model, we find that the FS is proportional to $L^2\ln L$ in the gapless phase, while $L^2$ in the gapped phase. Therefore, the extra dimension of $\ln L$ can be used as a characteristic of the gapless phase.

4 pages, 1 figure, final version to appear in EPL

References in corpus (25)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Mixed-state fidelity and quantum criticality at finite temperature
• Fidelity susceptibility, scaling, and universality in quantum critical phenomena
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Quantum fidelity and quantum phase transitions in matrix product states
• Quantum phase transitions and quantum fidelity in free fermion graphs
• Ground-state fidelity in one-dimensional gapless model
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Fidelity analysis of topological quantum phase transitions
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Quantum criticality of the Lipkin-Meshkov-Glick Model in terms of fidelity susceptibility
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Fidelity Between Partial States as Signature of Quantum Phase Transitions
• Ground state fidelity and quantum phase transitions in free Fermi systems
• Quantum Fidelity and Thermal Phase Transitions
• Operator fidelity susceptibility: an indicator of quantum criticality
• Fidelity approach to Gaussian transitions
• Operator fidelity susceptibility, decoherence and quantum criticality
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Fidelity susceptibility and quantum adiabatic condition in thermodynamic limits

Cited by in corpus (46)

• Nonequilibrium dynamics of closed interacting quantum systems
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Fidelity approach to quantum phase transitions
• Quantum enhanced measurements without entanglement
• Quench dynamics near a quantum critical point
• Quantum Critical Scaling of Fidelity Susceptibility
• Interaction effects and quantum phase transitions in topological insulators
• Universal nonequilibrium quantum dynamics in imaginary time
• Coherent and dissipative dynamics at quantum phase transitions
• Quench dynamics near a quantum critical point: application to the sine-Gordon model
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Unsupervised identification of topological order using predictive models
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Hamiltonian Learning for Quantum Error Correction
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Fidelity susceptibility in the two-dimensional transverse field Ising and XXZ models
• Oscillating fidelity susceptibility near a quantum multicritical point
• Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
• Automatic differentiation of dominant eigensolver and its applications in quantum physics
• Gauge-theoretic origin of Rydberg quantum spin liquids
• Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
• Fidelity and superconductivity in two-dimensional t-J models
• General Quantum Fidelity Susceptibilities for the J1-J2 Chain
• Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model
• A Fidelity Study of the Superconducting Phase Diagram in the 2D Single-band Hubbard Model
• From Classical to Quantum Information Geometry: A Guide for Physicists
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Quantum phase transition between topologically distinct quantum critical points
• Fidelity Study of Superconductivity in Extended Hubbard Models
• Topological edge modes and phase transition in the critical fermionic chain with long-range interaction
• Magnetic, thermodynamic, and dynamical properties of the three-dimensional fermionic Hubbard model: A comprehensive Monte Carlo study
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Fidelity susceptibility of one-dimensional models with twisted boundary conditions
• Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study
• Sudden quenching in the Kitaev honeycomb model: Study of defect and heat generation
• Dynamical phase transition and scaling in the chiral clock Potts chain
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Nonequilibrium dynamical renormalization group: Dynamical crossover from weak to infinite randomness in the transverse-field Ising chain
• Classification and emergence of quantum spin liquids in chiral Rydberg models
• Nonadiabatic stationary behaviour in a driven low-dimensional gapped system
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators
• Precision magnetometry exploiting excited state quantum phase transitions
• Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model
• Emergent dipole field theory in atomic ladders
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions