A Commuting Projector Model with a Non-zero Quantized Hall conductance

TL;DR

This paper constructs an exactly solvable lattice model for 2+1D SPT phases with non-zero Hall conductance, overcoming previous no-go theorems by using a rotor model with infinite states per site.

Contribution

It introduces a new commuting projector model for non-zero Hall conductance by ungauging a lattice rotor model, expanding the class of exactly solvable topological phases.

Findings

Confirmed non-zero Hall conductance via Chern number calculation.

Constructed a Hamiltonian with mutually commuting local projectors.

Demonstrated evasion of the no-go theorem for non-zero Hall conductance models.

Abstract

By ungauging a recently discovered lattice rotor model for Chern-Simons theory, we create an exactly soluble path integral on spacetime lattice for $U^\kappa(1)$ Symmetry Protected Topological (SPT) phases in $2+1$ dimensions with a non-zero Hall conductance. We then convert the path integral on a $2+1$d spacetime lattice into a $2$d Hamiltonian lattice model, and show that the Hamiltonian consists of mutually commuting local projectors. We confirm the non-zero Hall conductance by calculating the Chern number of the exact ground state. It has recently been suggested that no commuting projector model can host a nonzero Hall conductance. We evade this no-go theorem by considering a rotor model, with a countably infinite number of states per site.