We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this, we strengthen a previous result by establishing QMA-completeness for approximating the ground energy of the Bose-Hubbard model on simple graphs. Using a connection between the XY and Bose-Hubbard models that we exploited in previous work, this establishes QMA-completeness of the XY model.
@article{arxiv.1503.07083,
title = {Complexity of the XY antiferromagnet at fixed magnetization},
author = {Andrew M. Childs and David Gosset and Zak Webb},
journal= {arXiv preprint arXiv:1503.07083},
year = {2017}
}