Fidelity, dynamic structure factor, and susceptibility in critical phenomena

Abstract

Motivated by the growing importance of fidelity in quantum critical phenomena, we establish a general relation between fidelity and structure factor of the driving term in a Hamiltonian through a newly introduced concept: fidelity susceptibility. Our discovery, as shown by some examples, facilitates the evaluation of fidelity in terms of susceptibility using well developed techniques such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium.

4 pages, 2 figures, final version accepted by PRE

References in corpus (3)

• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Mixed-state fidelity and quantum criticality at finite temperature
• Quantum phase transitions and quantum fidelity in free fermion graphs

Cited by in corpus (37)

• 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
• Ground-state fidelity in one-dimensional gapless model
• Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Quantum Monte Carlo simulations of fidelity at magnetic quantum phase transitions
• Bures metric over thermal state manifolds and quantum criticality
• 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
• Direct observation of quantum criticality in Ising spin chains
• Fidelity Between Partial States as Signature of Quantum Phase Transitions
• Quantum Fidelity and Thermal Phase Transitions
• Fidelity approach to the disordered quantum XY model
• Operator fidelity susceptibility: an indicator of quantum criticality
• The fidelity approach to the Hubbard model
• Fidelity in topological quantum phases of matter
• Reduced fidelity susceptibility and its finite-size scaling behaviors
• Fidelity approach to Gaussian transitions
• Operator fidelity susceptibility, decoherence and quantum criticality
• Fidelity, fidelity susceptibility and von Neumann entropy to characterize the phase diagram of an extended Harper model
• Reduced fidelity in topological quantum phase transitions
• Geometric phases and quantum phase transitions
• Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase
• Quantum instability and edge entanglement in a quasi-long-range order
• Scaling of the fidelity susceptibility in a disordered quantum spin chain
• Ground-state fidelity of Luttinger liquids: A wave functional approach
• Quantum phase transition in the one-dimensional period-two and uniform compass model
• Quantum phase transitions in a two-dimensional quantum XYX model: Ground-state fidelity and entanglement
• Fidelity and superconductivity in two-dimensional t-J models
• Thermal states of the Kitaev honeycomb model: a Bures metric analysis
• Ground-state fidelity in the BCS-BEC crossover
• Density-functional fidelity approach to quantum phase transitions
• Partial-state fidelity and quantum phase transitions induced by continuous level crossing
• Entanglement and fidelity signatures of quantum phase transitions in spin liquid models
• Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model