Z2 topological invariants in two dimensions from quantum Monte Carlo

Thomas C. Lang, Andrew M. Essin, Victor Gurarie, and Stefan Wessel
Phys. Rev. B 87, 205101 – Published 1 May 2013

Abstract

We employ quantum Monte Carlo techniques to calculate the Z2 topological invariant in a two-dimensional model of interacting electrons that exhibits a quantum spin Hall topological insulator phase. In particular, we consider the parity invariant for inversion-symmetric systems, which can be obtained from the bulk's imaginary-time Green's function after an appropriate continuation to zero frequency. This topological invariant is used here in order to study the trivial-band to topological-insulator transitions in an interacting system with spin-orbit coupling and an explicit bond dimerization. We discuss the accessibility and behavior of this topological invariant within quantum Monte Carlo simulations.

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  • Received 25 March 2013

DOI:https://doi.org/10.1103/PhysRevB.87.205101

©2013 American Physical Society

Authors & Affiliations

Thomas C. Lang1,2,3,4, Andrew M. Essin5, Victor Gurarie5, and Stefan Wessel2,3,4

  • 1Department of Physics, Boston University, Boston, Massachusetts 02215, USA
  • 2Institute for Theoretical Solid State Physics, RWTH Aachen University, Aachen, Germany
  • 3JARA-HPC High Performance Computing
  • 4JARA-FIT Fundamentals of Future Information Technology
  • 5Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

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Issue

Vol. 87, Iss. 20 — 15 May 2013

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