Generalised ansatz for continuous Matrix Product States

TL;DR

This paper introduces a generalized continuous Matrix Product State (cMPS) ansatz capable of representing the continuum limit of any Matrix Product State (MPS), overcoming previous limitations by incorporating a sum over boundary conditions.

Contribution

The authors propose a new cMPS ansatz that includes a sum over boundary conditions, enabling it to express the continuum limit of any MPS, which was not possible with previous formulations.

Findings

The generalized ansatz can represent the continuum limit of any MPS.

It includes a sum of cMPS with different boundary conditions.

Examples demonstrate the effectiveness of the new ansatz.

Abstract

Recently it was shown that continuous Matrix Product States (cMPS) cannot express the continuum limit state of any Matrix Product State (MPS), according to a certain natural definition of the latter. The missing element is a projector in the transfer matrix of the MPS. Here we provide a generalised ansatz of cMPS that is capable of expressing the continuum limit of any MPS. It consists of a sum of cMPS with different boundary conditions, each attached to an ancilla state. This new ansatz can be interpreted as the concatenation of a state which is at the closure of the set of cMPS together with a standard cMPS. The former can be seen as a cMPS in the thermodynamic limit, or with matrices of unbounded norm. We provide several examples and discuss the result.