Matrix Product States for Trial Quantum Hall States

TL;DR

This paper presents an exact matrix-product-state representation for a broad class of fractional quantum Hall states, linking entanglement spectra to conformal field theory and providing numerical benchmarks across geometries.

Contribution

It introduces a novel MPS formalism for FQH states derived from conformal field theory correlators, enabling efficient analysis of their entanglement and edge properties.

Findings

Exact MPS representations for various FQH states including Moore-Read and Gaffnian

Demonstrated the connection between entanglement spectrum and edge modes

Provided numerical benchmarks validating the MPS approach

Abstract

We obtain an exact matrix-product-state (MPS) representation of a large series of fractional quantum Hall (FQH) states in various geometries of genus 0. The states in question include all paired k=2 Jack polynomials, such as the Moore-Read and Gaffnian states, as well as the Read-Rezayi k=3 state. We also outline the procedures through which the MPS of other model FQH states can be obtained, provided their wavefunction can be written as a correlator in a 1+1 conformal field theory (CFT). The auxiliary Hilbert space of the MPS, which gives the counting of the entanglement spectrum, is then simply the Hilbert space of the underlying CFT. This formalism enlightens the link between entanglement spectrum and edge modes. Properties of model wavefunctions such as the thin-torus root partitions and squeezing are recast in the MPS form, and numerical benchmarks for the accuracy of the new MPS prescription in various geometries are provided.