We use the half-filled zeroth Landau level in graphene as a regularization scheme to study the physics of the SO(5) non-linear sigma model subject to a Wess-Zumino-Witten topological term in 2+1 dimensions. As shown by Ippoliti et al. [PRB 98, 235108 (2019)], this approach allows for negative sign free auxiliary field quantum Monte Carlo simulations. The model has a single free parameter, U0, that monitors the stiffness. Within the parameter range accessible to negative sign free simulations, we observe an ordered phase in the large U0 or stiff limit. Remarkably, upon reducing U0 the magnetization drops substantially, and the correlation length exceeds our biggest system sizes, accommodating 100 flux quanta. The implications of our results for deconfined quantum phase transitions between valence bond solids and anti-ferromagnets are discussed.
@article{arxiv.2003.08368,
title = {Phases of the (2+1) dimensional SO(5) non-linear sigma model with topological term},
author = {Zhenjiu Wang and Michael P. Zaletel and Roger S. K. Mong and Fakher F. Assaad},
journal= {arXiv preprint arXiv:2003.08368},
year = {2021}
}