Fidelity analysis of topological quantum phase transitions

2008/03/31 by Damian F. Abasto, Alioscia Hamma, Paolo Zanardi · 4 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computer science #Exploit #Fidelity #Geometry #Mathematics #Metric (unit) #Opinion Dynamics and Social Influence #Phase (matter) #Phase transition #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Scaling #Statistical physics #Tensor (intrinsic definition) #Theoretical physics #Topological order #Topology (electrical circuits) #quant-ph

paper · pdf · doi:10.1103/physreva.78.010301

published as Phys. Rev. A 78, 010301(R), 2008. · 4 pages

arxiv created 2008/05/12 · openalex publication_date 2008/07/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We apply the fidelity metric approach to analyze two recently introduced models that exhibit a quantum phase transition to a topologically ordered phase. These quantum models have a known connection to classical statistical mechanical models; we exploit this mapping to obtain the scaling of the fidelity metric tensor near criticality. The topological phase transitions manifest themselves in divergences of the fidelity metric across the phase boundaries. These results provide evidence that the fidelity approach is a valuable tool to investigate novel phases lacking a clear characterization in terms of local order parameters.

Citations

• Lectures on Phase Transitions and the Renormalization Group
• From quantum mechanics to classical statistical physics: Generalized Rokhsar–Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition
• Decay of Loschmidt Echo Enhanced by Quantum Criticality
• Topological phases and topological entropy of two-dimensional systems with finite correlation length
• Ground State Fidelity from Tensor Network Representations
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
• Entanglement, fidelity, and topological entropy in a quantum phase transition to topological order
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction
• Quantum Critical Scaling of the Geometric Tensors
• Ground-state fidelity in one-dimensional gapless models
• Fault-tolerant quantum computation by anyons

Cited by

• Entanglement modes and topological phase transitions in superconductors
• Reduced fidelity in the Kitaev honeycomb model
• Quantum phase transition in easy-axis antiferromagnetic Heisenberg spin-1 chain
• Boundary fidelity and entanglement in the symmetry protected topological phase of the SSH model