Fidelity susceptibility near topological phase transitions in quantum walks

S. Panahiyan, W. Chen, and S. Fritzsche
Phys. Rev. B 102, 134111 – Published 16 October 2020

Abstract

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.

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  • Received 20 July 2020
  • Revised 30 September 2020
  • Accepted 30 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.134111

©2020 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

S. Panahiyan1,2,3,*, W. Chen4,†, and S. Fritzsche1,2,3,‡

  • 1Helmholtz-Institut Jena, Fröbelstieg 3, D-07743 Jena, Germany
  • 2GSI Helmholtzzentrum für Schwerionenforschung, D-64291 Darmstadt, Germany
  • 3Theoretisch-Physikalisches Institut, Friedrich-Schiller-University Jena, D-07743 Jena, Germany
  • 4Department of Physics, PUC-Rio, 22451-900 Rio de Janeiro, Brazil

  • *shahram.panahiyan@uni-jena.de
  • wchen@puc-rio.br
  • s.fritzsche@gsi.de

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Issue

Vol. 102, Iss. 13 — 1 October 2020

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