Quantum Monte Carlo study of strange correlator in interacting topological insulators

Abstract

Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that most of the topological indices defined for free electron systems are very likely unsuitable for interacting cases. In this work, we demonstrate that the strange correlator is a sensitive diagnosis to detect SPT states in interacting systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we investigate the interaction-driven quantum phase transition in the Kane-Mele-Hubbard model. The transition from the quantum spin Hall insulator at weak interaction to an antiferromagnetic Mott insulator at strong interaction can be readily detected by the momentum space behavior of the strange correlator in single-particle, spin, and pairing sectors. The interaction effects on the symmetry-protected edge states in various sectors, i.e., the helical Luttinger liquid behavior, are well captured in the QMC measurements of strange correlators. Moreover, we demonstrate that the strange correlator is technically easier to implement in QMC and more robust in performance than other proposed numerical diagnoses for interacting topological states, as only static correlations are needed. The attempt in this work paves the way for using the strange correlator to study interaction-driven topological phase transitions in fermionic as well as bosonic systems.

10 pages, 9 figures, 1 appendix

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• Universal Features of Higher-Form Symmetries at Phase Transitions
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• Topological invariants for interacting topological insulators: II. Breakdown of the Green's function formalism
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• Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: application to the square lattice bilayer and honeycomb lattice
• Topological invariants for interacting topological insulators: I. Efficient numerical evaluation scheme and implementations
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• Topological phase in $1D$ topological Kondo insulator: $Z_2$ topological insulator, Haldane-like phase and Kondo breakdown
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• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
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• Phase transitions of the dimerized Kane-Mele model with/without the strong interaction
• Spurious Strange Correlators in Symmetry-Protected Topological Phases