2020/07/21 by S. Panahiyan, W. Chen, Wei Chen +1
Mathematics · Physics and Astronomy · #Mathematics #Phase transition #Physics #Position and momentum space #Quantum #Quantum and electron transport phenomena #Quantum critical point #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physrevb.102.134111
published as Phys. Rev. B 102, 134111 (2020) · 12 pages, 10 figures
arxiv created 2020/07/21 · openalex publication_date 2020/10/16 · arxiv updated 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The notion of fidelity susceptibility, introduced within the context of quantum metric tensor, has been an important quantity to characterize the criticality near quantum phase transitions. We demonstrate that for topological phase transitions in Dirac models, provided the momentum space is treated as the manifold of the quantum metric, the fidelity susceptibility coincides with the curvature function whose integration gives the topological invariant. Thus the quantum criticality of the curvature function near a topological phase transition also describes the criticality of the fidelity susceptibility, and the correlation length extracted from the curvature function also gives a momentum scale over which the fidelity susceptibility decays. To map out the profile and criticality of the fidelity susceptibility, we turn to quantum walks that simulate one-dimensional class BDI and two- dimensional class D Dirac models and demonstrate their accuracy in capturing the critical exponents and scaling laws near topological phase transitions.