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.

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

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• Scaling of the fidelity susceptibility in a disordered quantum spin chain
• Quantum kernels to learn the phases of quantum matter
• From Classical to Quantum Information Geometry: A Guide for Physicists
• Ground-state fidelity in the BCS-BEC crossover
• Fidelity susceptibility and general quench near an anisotropic quantum critical point
• Fidelity Study of Superconductivity in Extended Hubbard Models
• Finite-Temperature Fidelity-Metric Approach to the Lipkin-Meshkov-Glick Model
• Dipolar Bose-Hubbard Model in finite-size real-space cylindrical lattices
• Information geometry and synchronization phase transition in Kuramoto model
• A Quantum Fidelity Study of the Anisotropic Next-Nearest-Neighbour Triangular Lattice Heisenberg Model
• Entanglement and fidelity across quantum phase transitions in locally perturbed topological codes with open boundaries
• Comparing quantum complexity and quantum fidelity
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions