Phases of the ($2+1$) Dimensional SO(5) Nonlinear Sigma Model with Topological Term

Phases of the ( $2 + 1$ ) Dimensional SO(5) Nonlinear Sigma Model with Topological Term

Zhenjiu Wang, Michael P. Zaletel, Roger S. K. Mong, and Fakher F. Assaad

Phys. Rev. Lett. 126, 045701 – Published 29 January 2021

Abstract

We use the half-filled zeroth Landau level in graphene as a regularization scheme to study the physics of the SO(5) nonlinear sigma model subject to a Wess-Zumino-Witten topological term in $2 + 1$ dimensions. As shown by Ippoliti et al. [Phys. Rev. B 98, 235108 (2019)], this approach allows for negative sign free auxiliary field quantum Monte Carlo simulations. The model has a single free parameter $U_{0}$ that monitors the stiffness. Within the parameter range accessible to negative sign free simulations, we observe an ordered phase in the large $U_{0}$ or stiff limit. Remarkably, upon reducing $U_{0}$ 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 antiferromagnets are discussed.

Received 26 March 2020
Accepted 5 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.045701

Physics Subject Headings (PhySH)

Critical exponents Effective field theory Landau levels Quantum criticality

Condensed Matter, Materials & Applied PhysicsStatistical Physics & ThermodynamicsGeneral PhysicsParticles & Fields

Authors & Affiliations

Zhenjiu Wang^1,*, Michael P. Zaletel², Roger S. K. Mong³, and Fakher F. Assaad^1,4,†

¹Institut für Theoretische Physik und Astrophysik, Universität Würzburg, 97074 Würzburg, Germany
²Department of Physics, University of California, Berkeley, California 94720, USA
³Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
⁴Würzburg-Dresden Cluster of Excellence ct.qmat, Am Hubland, D-97074 Würzburg, Germany