Ground state fidelity and quantum phase transitions in free Fermi systems

Abstract

We compute the fidelity between the ground states of general quadratic fermionic hamiltonians and analyze its connections with quantum phase transitions. Each of these systems is characterized by a $L\times L$ real matrix whose polar decomposition, into a non-negative $\Lambda$ and a unitary $T$, contains all the relevant ground state (GS) information. The boundaries between different regions in the GS phase diagram are given by the points of, possibly asymptotic, singularity of $\Lambda$. This latter in turn implies a critical drop of the fidelity function. We present general results as well as their exemplification by a model of fermions on a totally connected graph.

4 pages, 2 figures

References in corpus (1)

• Quantum phase transitions and quantum fidelity in free fermion graphs

Cited by in corpus (52)

• Fidelity approach to quantum phase transitions
• Quantum critical scaling of the geometric tensors
• Quantum enhanced measurements without entanglement
• Geometry of quantum phase transitions
• Thermometry in the quantum regime: Recent theoretical progress
• A short review on entanglement in quantum spin systems
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• Quantum metrology in Lipkin-Meshkov-Glick critical systems
• Unsupervised phase discovery with deep anomaly detection
• Quantum mechanical and information theoretic view on classical glass transitions
• Quantum Fidelity and Thermal Phase Transitions
• Fidelity approach to the disordered quantum XY model
• The fidelity approach to the Hubbard model
• Scaling dimension of fidelity susceptibility in quantum phase transitions
• Fidelity in topological quantum phases of matter
• Information geometric methods for complexity
• Finite-Size Geometric Entanglement from Tensor Network Algorithms
• Scaling of the fidelity susceptibility in a disordered quantum spin chain
• Spectral function and fidelity susceptibility in quantum critical phenomena
• Ground-state fidelity of Luttinger liquids: A wave functional approach
• Spontaneous symmetry breaking and bifurcations in ground state fidelity for quantum lattice systems
• In and out of equilibrium quantum metrology with mean-field quantum criticality
• Spin-1/2 Heisenberg ladder: variation of entanglement and fidelity measures close to quantum critical points
• General Quantum Fidelity Susceptibilities for the J1-J2 Chain
• Renyi relative entropies and renormalization group flows
• Phase diagram of a Bose-Fermi mixture in a one-dimensional optical lattice in terms of fidelity and entanglement
• Universal sub-leading terms in ground state fidelity
• Entanglement modes and topological phase transitions in superconductors
• Quantum chaos and operator fidelity metric
• Thermal states of the Kitaev honeycomb model: a Bures metric analysis
• Visualizing quantum phase transitions in the XXZ model via the quantum steering ellipsoid
• Many-body reduced fidelity susceptibility in Lipkin-Meshkov-Glick model
• Entanglement, fidelity, and quantum phase transition in antiferromagnetic-ferromagnetic alternating Heisenberg chain
• Scale vs Conformal invariance from Entanglement Entropy
• Fidelity spectrum and phase transitions of quantum systems
• Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model
• Finite-temperature quantum criticality in a complex-parameter plane
• Unsupervised mapping of phase diagrams of 2D systems from infinite projected entangled-pair states via deep anomaly detection
• Simulating continuous symmetry models with discrete ones
• Detection of quantum phase boundary at finite temperatures in integrable spin models
• Unsupervised learning of phase transitions via modified anomaly detection with autoencoders
• Ground-State Fidelity and Kosterlitz-Thouless Phase Transition for Spin 1/2 Heisenberg Chain with Next-to-the-Nearest-Neighbor Interaction
• Holographic encoding of universality in corner spectra
• Complexity and instability of quantum motion near a quantum phase transition
• Scaling behavior for a class of quantum phase transitions
• Groundstate fidelity phase diagram of the fully anisotropic two-leg spin-1/2 XXZ ladder
• Relation between equilibrium quantum phase transitions and dynamical quantum phase transitions in two-band systems
• Quantum Renyi relative entropies on a spin chain with interface defects
• Signature of quantum phase transition manifested in quantum fidelity at finite temperature
• Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing
• Gravity dualities of quantum distances
• Exploring Many-Body Quantum Geometry Beyond the Quantum Metric with Correlation Functions: A Time-Dependent Perspective