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

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Materials Science

Background:

• Graphene's half-filled zeroth Landau level offers a unique regularization scheme.
• The SO(5) nonlinear sigma model with a Wess-Zumino-Witten term is crucial for studying certain quantum phases.

Purpose of the Study:

• To investigate the physics of the SO(5) nonlinear sigma model in 2+1 dimensions using graphene.
• To explore the role of a topological term and stiffness parameter (U0) on the model's phases.
• To enable negative sign-free auxiliary field quantum Monte Carlo simulations.

Main Methods:

• Utilizing the half-filled zeroth Landau level in graphene as a regularization scheme.
• Employing negative sign-free auxiliary field quantum Monte Carlo simulations.
• Systematically varying the stiffness parameter U0.

Main Results:

• An ordered phase was observed in the large U0 (stiff) limit.
• Reducing U0 led to a significant drop in magnetization.
• Correlation lengths grew beyond system sizes of 100 flux quanta as U0 decreased.

Conclusions:

• The study provides insights into the behavior of the SO(5) model under varying stiffness.
• Results suggest implications for understanding deconfined quantum phase transitions.
• The findings are relevant to transitions between valence bond solids and antiferromagnets.