Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction

TL;DR

This paper develops a matrix product state representation for the one-dimensional Bose gas with delta interaction, bridging lattice Bethe ansatz states and continuum limits, simplifying the complex bosonic system.

Contribution

It introduces a continuous matrix product ansatz derived from lattice models, providing an exact representation for the Lieb-Liniger model in the continuum limit.

Findings

Exact continuous matrix product states obtained from lattice Bethe ansatz

Reduction of the bosonic system to a five-vertex model

Demonstrates the importance of F-matrices in the continuum limit

Abstract

We study a matrix product representation of the Bethe ansatz state for the Lieb-Linger model describing the one-dimensional Bose gas with delta-function interaction. We first construct eigenstates of the discretized model in the form of matrix product states using the algebraic Bethe ansatz. Continuous matrix product states are then exactly obtained in the continuum limit with a finite number of particles. The factorizing $F$-matrices in the lattice model are indispensable for the continuous matrix product states and lead to a marked reduction from the original bosonic system with infinite degrees of freedom to the five-vertex model.