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

## TL;DR

This paper introduces an exactly solvable 2D topological insulator model using commuting-projector Hamiltonians, capturing edge physics and many-body invariants, and extending understanding of topological phases with symmetries.

## Contribution

The authors develop a new commuting-projector model for 2D topological insulators that incorporates interactions and symmetries, providing explicit edge and bulk invariant characterizations.

## Key findings

- Model reproduces boundary physics of topological insulators.
- Identifies bulk invariants related to $ ext{CP}$ symmetry.
- Provides a framework for many-body topological 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 $\mathcal{CP}$ symmetry, leading to intuitive interpretations of the bulk invariant for a $\mathcal{CP}$-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.