2013/07/31 by Hsiang-Hsuan Hung, Victor Chua, Lei Wang +1 · 1 citation
Physics and Astronomy · #Advanced Condensed Matter Physics #Chern class #Fermion #Invariant (physics) #Lattice (music) #Monte Carlo method #Phase transition #Physics #Quantum #Quantum Monte Carlo #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Symmetry protected topological order #Thermodynamic limit #Topological Materials and Phenomena #Topological order #Topology (electrical circuits) #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.89.235104
published as Phys. Rev. B 89, 235104 (2014) · 15 pages, revised with detailed information
openalex publication_date 2014/06/04 · arxiv created 2014/06/08 · arxiv updated 2014/06/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to 2\ifmmode×\else\texttimes\fi182 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 C_\ensuremathσ 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.