skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence

Abstract

The fidelity between two infinitesimally close states and the fidelity susceptibility of a system are known to detect quantum phase transitions. Here we show that the k-space fidelity between two states far from each other and taken deep inside (bulk) of two phases, generically vanishes at the k-points where there are gapless points in the energy spectrum that give origin to the lines (edges) separating the phases in the phase diagram. We consider a general case of two-band models and present a sufficient condition for the existence of gapless points, given there are pairs of parameter points for which the fidelity between the corresponding states is zero. By presenting an explicit counter-example, we show that the sufficient condition is not necessary. Further, we show that, unless the set of parameter points is suitably constrained, the existence of gapless points generically implies accompanied pairs of parameter points with vanishing fidelity. Also, we show the connection between the vanishing fidelity and gapless points on a number of concrete examples (topological triplet superconductor, topological insulator, 1d Kitaev model of spinless fermions, BCS superconductor, Ising model in a transverse field, graphene and Haldane Chern insulator), as well as for the more general case ofmore » Dirac-like Hamiltonians. We also briefly discuss the relation between the vanishing fidelity and gapless points at finite temperatures.« less

Authors:
 [1];  [1]
  1. CeFEMA, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal)
Publication Date:
OSTI Identifier:
22852378
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 401; Other Information: © 2018 Elsevier Inc. All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ENERGY SPECTRA; FERMIONS; GRAPHENE; HAMILTONIANS; ISING MODEL; PHASE DIAGRAMS; PHASE TRANSFORMATIONS; SUPERCONDUCTORS; TOPOLOGY; TRIPLETS

Citation Formats

Sacramento, P.D., E-mail: pdss@cefema.tecnico.ulisboa.pt, Mera, B., Instituto de Telecomunicações, 1049-001 Lisboa, Paunković, N., Instituto de Telecomunicações, 1049-001 Lisboa, and Departmento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa. Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence. United States: N. p., 2019. Web. doi:10.1016/J.AOP.2018.11.021.
Sacramento, P.D., E-mail: pdss@cefema.tecnico.ulisboa.pt, Mera, B., Instituto de Telecomunicações, 1049-001 Lisboa, Paunković, N., Instituto de Telecomunicações, 1049-001 Lisboa, & Departmento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa. Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence. United States. https://doi.org/10.1016/J.AOP.2018.11.021
Sacramento, P.D., E-mail: pdss@cefema.tecnico.ulisboa.pt, Mera, B., Instituto de Telecomunicações, 1049-001 Lisboa, Paunković, N., Instituto de Telecomunicações, 1049-001 Lisboa, and Departmento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa. Fri . "Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence". United States. https://doi.org/10.1016/J.AOP.2018.11.021.
@article{osti_22852378,
title = {Vanishing k-space fidelity and phase diagram’s bulk–edge–bulk correspondence},
author = {Sacramento, P.D., E-mail: pdss@cefema.tecnico.ulisboa.pt and Mera, B. and Instituto de Telecomunicações, 1049-001 Lisboa and Paunković, N. and Instituto de Telecomunicações, 1049-001 Lisboa and Departmento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa},
abstractNote = {The fidelity between two infinitesimally close states and the fidelity susceptibility of a system are known to detect quantum phase transitions. Here we show that the k-space fidelity between two states far from each other and taken deep inside (bulk) of two phases, generically vanishes at the k-points where there are gapless points in the energy spectrum that give origin to the lines (edges) separating the phases in the phase diagram. We consider a general case of two-band models and present a sufficient condition for the existence of gapless points, given there are pairs of parameter points for which the fidelity between the corresponding states is zero. By presenting an explicit counter-example, we show that the sufficient condition is not necessary. Further, we show that, unless the set of parameter points is suitably constrained, the existence of gapless points generically implies accompanied pairs of parameter points with vanishing fidelity. Also, we show the connection between the vanishing fidelity and gapless points on a number of concrete examples (topological triplet superconductor, topological insulator, 1d Kitaev model of spinless fermions, BCS superconductor, Ising model in a transverse field, graphene and Haldane Chern insulator), as well as for the more general case of Dirac-like Hamiltonians. We also briefly discuss the relation between the vanishing fidelity and gapless points at finite temperatures.},
doi = {10.1016/J.AOP.2018.11.021},
url = {https://www.osti.gov/biblio/22852378}, journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = ,
volume = 401,
place = {United States},
year = {2019},
month = {2}
}