Commuting-projector Hamiltonians for 2D topological insulators: edge physics and many-body invariants

Abstract

Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that describes an interacting yet exactly solvable 2D topological insulator. We explicitly show that both the gapped and gapless boundaries of our model are consistent with those of band-theoretic, weakly interacting topological insulators. Interestingly, on certain lattices our time-reversal-symmetric models also enjoy $\mathcal{C}\mathcal{P}$ symmetry, leading to intuitive interpretations of the bulk invariant for a $\mathcal{C}\mathcal{P}$-symmetric topological insulator upon putting the system on a Klein bottle. We also briefly discuss how these many-body invariants may be able to characterize models with only time-reversal symmetry.

19+9 pages, 22 Figures

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• Anomalous localization at the boundary of an interacting topological insulator
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• Exactly solvable lattice models for interacting electronic insulators in two dimensions
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Universal contributions to charge fluctuations in spin chains at finite temperature
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase