Generalised ansatz for continuous Matrix Product States
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.
Cite
@article{arxiv.1908.09761,
title = {Generalised ansatz for continuous Matrix Product States},
author = {Maria Balanzó-Juandó and Gemma De las Cuevas},
journal= {arXiv preprint arXiv:1908.09761},
year = {2020}
}
Comments
v2: major revision; 11 pages and 1 figure; close to published version. v1: 10 pages