Exactly solvable lattice models for interacting electronic insulators in two dimensions

Abstract

In the past decade, tremendous efforts have been made towards understanding fermionic symmetry protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is still unclear how to construct an exactly solvable model with a finite dimensional Hilbert space in general. In this paper, we give a lattice model construction and classification for 2D interacting electronic insulators. Based on the physical picture of ${\mathrm{U}(1)}_f$-charge decorations, we illustrate the key idea by considering the well known 2D interacting topological insulator. Then we generalize our construction to an arbitrary 2D interacting electronic insulator with symmetry $G_f={\mathrm{U}(1)}_f{⋊}_{{\rho }_1,{\omega }_2}G$, where ${\mathrm{U}(1)}_f$ is the charge conservation symmetry and ${\rho }_1,{\omega }_2$ are additional data which fully characterize the group structure of $G_f$. Finally we study more examples, including the full interacting classification of 2D crystalline topological insulators.

6+11 pages, 2 figures, 3 tables

References in corpus (3)

• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Exactly solvable models for U(1) symmetry-enriched topological phases

Cited by in corpus (4)

• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Frustration-free free fermions
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases