Weakly interacting topological insulators: Quantum criticality and the renormalization group approach

Wei Chen
Phys. Rev. B 97, 115130 – Published 14 March 2018

Abstract

For D-dimensional weakly interacting topological insulators in certain symmetry classes, the topological invariant can be calculated from a D- or (D+1)-dimensional integration over a certain curvature function that is expressed in terms of single-particle Green's functions. Based on the divergence of curvature function at the topological phase transition, we demonstrate how a renormalization group approach circumvents these integrations and reduces the necessary calculation to that for the Green's function alone, rendering a numerically efficient tool to identify topological phase transitions in a large parameter space. The method further unveils a number of statistical aspects related to the quantum criticality in weakly interacting topological insulators, including correlation function, critical exponents, and scaling laws, that can be used to characterize the topological phase transitions driven by either interacting or noninteracting parameters. We use 1D class BDI and 2D class A Dirac models with electron-electron and electron-phonon interactions to demonstrate these principles and find that interactions may change the critical exponents of the topological insulators.

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  • Received 2 January 2018

DOI:https://doi.org/10.1103/PhysRevB.97.115130

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wei Chen

  • Department of Physics, PUC-Rio, 22451-900 Rio de Janeiro, Brazil

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Issue

Vol. 97, Iss. 11 — 15 March 2018

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