Exactly Solvable Fermion Chain Describing a $\nu=1/3$ Fractional Quantum Hall State

TL;DR

This paper presents an exactly solvable fermion chain model that captures the properties of a $ u=1/3$ fractional quantum Hall state beyond the thin-torus approximation, enabling precise calculations of physical quantities.

Contribution

The authors introduce a novel exactly solvable fermion chain model for the $ u=1/3$ FQH state that allows for analytical computation of order parameters, correlation functions, and excitation gaps.

Findings

Ground state is unique per center of mass sector.

Ground state exhibits similarities to BCS and quantum spin-1 chains.

Analytical calculation of excitation gaps and compressibility.

Abstract

We introduce an exactly solvable fermion chain that describes a $\nu=1/3$ fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center of mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the variational method with matrix product ansatz, we analytically calculate excitation gaps and vanishing of the compressibility expected in the FQH state. We also show that the above results can be related to a $\nu=1/2$ bosonic FQH state.