Interaction effects on topological phase transitions via numerically exact quantum Monte Carlo calculations

Hsiang-Hsuan Hung, Victor Chua, Lei Wang, and Gregory A. Fiete
Phys. Rev. B 89, 235104 – Published 4 June 2014

Abstract

We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to 2×182 sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the Z2 invariant and spin Chern number Cσ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The Z2 invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the noninteracting limit, without any spontaneously symmetry breaking. The interaction-induced shift is nonperturbative in the interactions and cannot be captured within a “simple” self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the D3 symmetry of the lattice, and destabilize topological phases when the one-body terms break the D3 symmetry.

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  • Received 9 July 2013
  • Revised 16 May 2014

DOI:https://doi.org/10.1103/PhysRevB.89.235104

©2014 American Physical Society

Authors & Affiliations

Hsiang-Hsuan Hung1, Victor Chua1,*, Lei Wang2, and Gregory A. Fiete1

  • 1Department of Physics, The University of Texas at Austin, Austin, Texas, 78712, USA
  • 2Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland

  • *Department of Physics, The University of Illinois at Urbana-Champaign, Illinois, 61801, USA.

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Vol. 89, Iss. 23 — 15 June 2014

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