Numerical Contraction of the Tensor Network generated by the Algebraic Bethe Ansatz

TL;DR

This paper introduces a method to approximate eigenstates from the algebraic Bethe Ansatz using tensor network states, enabling direct calculation of physical observables like correlation functions.

Contribution

It presents a novel approach to represent Bethe Ansatz eigenstates as Matrix Product States, facilitating property extraction from complex quantum models.

Findings

Eigenstates can be approximated as Matrix Product States.

Correlation functions can be computed directly from the tensor network.

The method simplifies analysis of quantum integrable models.

Abstract

The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations. Whereas the spectrum is usually obtained directly, the eigenstates are available only in terms of complex mathematical expressions. This makes it very hard in general to extract properties from the states, like, for example, correlation functions. In our work, we apply the tools of Tensor Network States to describe the eigenstates approximately as Matrix Product States. From the Matrix Product State expression, we then obtain observables like correlation functions directly.