Solvable Lattice Hamiltonians with Fractional Hall Conductivity

TL;DR

This paper introduces a new class of lattice Hamiltonians that can be approximately solved to exhibit fractional Hall conductivity, providing a systematic method to bypass previous theoretical limitations.

Contribution

It presents a systematic construction of lattice Hamiltonians with fractional Hall effects, overcoming the Kapustin-Fidkowski no-go theorem and offering a generalizable approach.

Findings

Hamiltonians exhibit fractional Hall conductivity

Low energy sectors are controllably solvable

Method bypasses previous no-go theorems

Abstract

We construct a class of lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be controllably solved in their low energy sectors, through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem and is generalizable.