Fractional Quantum Hall States: Infinite Matrix Product Representation and its Implications

TL;DR

This paper introduces a new matrix product representation for fractional quantum Hall wavefunctions, providing insights into their structure, correlations, and entanglement properties, with implications for understanding topological quantum states.

Contribution

It offers a rigorous matrix product representation of Laughlin wavefunctions based on chiral quantum field theory correlators, revealing their factorization and correlation decay properties.

Findings

Proves bounds on chiral quantum field theory correlators

Demonstrates exponential decay of connected correlations

Establishes a gap in the entanglement spectrum on a thin cylinder

Abstract

We present a novel matrix product representation of the Laughlin and related fractional quantum Hall wavefunctions based on a rigorous version of the correlators of a chiral quantum field theory. This representation enables the quantitative control of the coefficients of the Laughlin wavefunction times an arbitrary monomial symmetric polynomial when expanded in a Slater determinant or permanent basis. It renders the properties, such as factorization and the renewal structure, inherent in such fractional quantum Hall wavefunctions transparent. We prove bounds on the correlators of the chiral quantum field theory and utilize this representation to demonstrate the exponential decay of connected correlations and a gap in the entanglement spectrum on a thin cylinder.