Fidelity in topological quantum phases of matter

Abstract

Quantum phase transitions that take place between two distinct topological phases remain an unexplored area for the applicability of the fidelity approach. Here, we apply this method to spin systems in two and three dimensions and show that the fidelity susceptibility can be used to determine the boundary between different topological phases particular to these models, while at the same time offering information about the critical exponent of the correlation length. The success of this approach relies on its independence on local order parameters or breaking symmetry mechanisms, with which non-topological phases are usually characterized. We also consider a topological insulator/superconducting phase transition in three dimensions and point out the relevant features of fidelity susceptibility at the boundary between these phases.

arXiv comment7 pages, 7 figures; added references; to appear on PRA

References in corpus (20)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Anyons in an exactly solved model and beyond
• Ground state overlap and quantum phase transitions
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• The Flux-Phase of the Half-Filled Band
• An exact chiral spin liquid with non-Abelian anyons
• A Measure of data-collapse for scaling
• 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
• Mosaic spin models with topological order
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Ground state fidelity and quantum phase transitions in free Fermi systems
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model
• The Wavefunction of an Anyon
• Thermal states of the Kitaev honeycomb model: a Bures metric analysis

Cited by in corpus (37)

• Fidelity approach to quantum phase transitions
• Quantum enhanced measurements without entanglement
• Geometry of quantum phase transitions
• Classifying and measuring the geometry of the quantum ground state manifold
• Abelian and Non-Abelian Quantum Geometric Tensor
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Momentum space metric, non-local operator, and topological insulators
• The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems
• Oscillating fidelity susceptibility near a quantum multicritical point
• Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models
• Reduced fidelity in topological quantum phase transitions
• Scaling of the fidelity susceptibility in a disordered quantum spin chain
• Automatic differentiation of dominant eigensolver and its applications in quantum physics
• Fidelity susceptibility of the anisotropic $XY$ model: The exact solution
• Quantum kernels to learn the phases of quantum matter
• Quenching in Chern insulators with satellite Dirac points: The fate of edge states
• Revealing Chern number from quantum metric
• 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
• Ground-state fidelity in the BCS-BEC crossover
• Fidelity Study of Superconductivity in Extended Hubbard Models
• Multipartite entanglement and quantum Fisher information in conformal field theories
• Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model
• Measure of the density of quantum states in information geometry and its application in the quantum multi-parameter estimation
• Entanglement susceptibility: Area laws and beyond
• The Loschmidt Index
• Hidden Symmetries, the Bianchi Classification and Geodesics of the Quantum Geometric Ground-State Manifolds
• Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals
• Resonance states in a cylindrical quantum dot with an external magnetic field
• Dipolar Bose-Hubbard Model in finite-size real-space cylindrical lattices
• A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model
• Information geometry and synchronization phase transition in Kuramoto model
• Measurement of arbitrary two-photon entanglement state with the photonic Faraday rotation
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
• Comparing quantum complexity and quantum fidelity