Matrix product states for trial quantum Hall states

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 MPSs of other model FQH states can be obtained, provided their wave function 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 wave functions 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.