Entropy and Exact Matrix Product Representation of the Laughlin Wave Function

TL;DR

This paper derives the von Neumann entropy for the Laughlin wave function, provides bounds on matrix sizes for exact representations, and proposes an analytical matrix product state using Clifford algebra, especially optimal at filling fraction nu=1.

Contribution

It introduces an analytical entropy expression and a matrix product state representation for the Laughlin wave function, advancing understanding of its entanglement and matrix size requirements.

Findings

Exact von Neumann entropy for nu=1

Upper bounds on entropy for nu=1/m

Asymptotically optimal matrix product state at nu=1

Abstract

An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for filling fraction nu=1. Also, for filling fraction nu=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix product state. An analytical matrix product state representation of this state is proposed in terms of representations of the Clifford algebra. For nu=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles.