One-dimensional lattice model with an exact matrix-product ground state describing the Laughlin wave function

TL;DR

This paper presents a one-dimensional lattice model with an exact matrix-product ground state that accurately describes Laughlin fractional quantum Hall states on a torus, providing analytical insights into their properties.

Contribution

It introduces a novel exactly solvable lattice Hamiltonian with a matrix-product ground state that captures key features of Laughlin FQH states, linking lattice models to continuum wave functions.

Findings

High overlap between the exact ground state and Laughlin wave function

Analytical calculation of density and correlation functions

Entanglement spectra reveal gapless edge states

Abstract

We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors $\nu=1/q$) on torus geometry. Surprisingly, the exactly solvable Hamiltonian has the same mathematical structure as that of the pseudopotential for the Laughlin wave function, and naturally derives the general properties of the Laughlin wave function such as the $Z_2$ properties of the FQH states and the fermion-boson relation. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using the matrix product method, density functions and correlation functions are calculated analytically. Especially, obtained entanglement spectra reflects gapless edge states as was discussed by Li and Haldane.