Universal sub-leading terms in ground state fidelity

Abstract

The study of the (logarithm of the) {\em fidelity} i.e., of the overlap amplitude, between ground states of Hamiltonians corresponding to different coupling constants, provides a valuable insight on critical phenomena. When the parameters are infinitesimally close, it is known that the leading term behaves as $O(L^{\alpha })$ ($L$ system size) where $\alpha$ is equal to the spatial dimension $d$ for gapped systems, and otherwise depends on the critical exponents. Here we show that when parameters are changed along a critical manifold, a sub-leading O(1) term can appear. This term, somewhat similar to the topological entanglement entropy, depends only on the system's universality class and encodes non-trivial information about the topology of the system. We relate it to universal $g$ factors and partition functions of (boundary) conformal field theory in $d=1$ and $d=2$ dimensions. Numerical checks are presented on the simple example of the XXZ chain.

revtex4, 2 pdf figures

References in corpus (16)

• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Topological Order and Conformal Quantum Critical Points
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• 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
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
• Fidelity analysis of topological quantum phase transitions
• Fidelity approach to quantum phase transitions: finite size scaling for quantum Ising model in a transverse field
• Fidelity approach to Gaussian transitions
• Ground-state fidelity of Luttinger liquids: A wave functional approach

Cited by in corpus (20)

• Fidelity approach to quantum phase transitions
• Shannon and entanglement entropies of one- and two-dimensional critical wave functions
• Rényi entropy of a line in two-dimensional Ising models
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Finite temperature fidelity susceptibility for one-dimensional quantum systems
• Universal behavior of a bipartite fidelity at quantum criticality
• Oscillating fidelity susceptibility near a quantum multicritical point
• Entanglement entropy between two coupled Tomonaga-Luttinger liquids
• Logarithmic corrections to the free energy from sharp corners with angle $2\pi$
• Universal fidelity near quantum and topological phase transitions in finite 1D systems
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• System-environment entanglement phase transitions
• Many-Body-Localization Transition : sensitivity to twisted boundary conditions
• Equilibration times in clean and noisy systems
• Exponential Orthogonality Catastrophe at the Anderson Metal-Insulator Transition
• Stabilizer Rényi Entropy and Conformal Field Theory
• Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks
• Quantum hypothesis testing in many-body systems
• Quench Dynamics in Confined 1+1-Dimensional Systems
• Quantum Fidelity of the Aubry-André Model and the Exponential Orthogonality Catastrophe