Solvable lattice model for (2+1)D bosonic topological insulator

Abstract

We construct an exactly sovable commuting projector Hamiltonian for (2+1)D bosonic topological insulator which is one of symmetry-protected topological (SPT) phases protected by U(1) and time-reversal ${\mathbb{Z}}_2^T$ symmetry, where the symmetry group is U(1)$⋊{\mathbb{Z}}_2^T$. The model construction is based on the decorated domain-wall interpretation of the $E_{\infty }$-page of a spectral sequence of a cobordism group that classifies the SPT phases in question. We demonstrate nontriviality of the model by showing an emergence of a Kramers doublet when the system is put on a semi-infinite cylinder $(-\infty ,0]\times S^1$ with an inserted $\pi$-flux. The surface anomaly manifests itself as a non-onsite representation of the U(1)$⋊{\mathbb{Z}}_2^T$ symmetry. Anomaly matching on a boundary is discussed within a simple boundary theory.

References in corpus (10)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Anomalies of discrete symmetries in various dimensions and group cohomology
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Microscopic Realization of 2-Dimensional Bosonic Topological Insulators