Continuous Matrix Product States for Quantum Fields

TL;DR

This paper introduces a continuum version of matrix product states, enabling the application of tensor network methods directly to quantum field theories in one dimension, exemplified by the Lieb-Liniger model.

Contribution

It develops a lattice-free continuum matrix product state framework, extending tensor network techniques to quantum fields without relying on discretization.

Findings

Successfully applied to the Lieb-Liniger model

Enables variational studies of continuum quantum systems

Bridges tensor networks and quantum field theory

Abstract

We define matrix product states in the continuum limit, without any reference to an underlying lattice parameter. This allows to extend the density matrix renormalization group and variational matrix product state formalism to quantum field theories and continuum models in 1 spatial dimension. We illustrate our procedure with the Lieb-Liniger model.