Symplectic N and time reversal in frustrated magnetism

TL;DR

This paper introduces a new large N approximation for quantum magnetism based on symplectic symmetry, capturing both antiferromagnetic and ferromagnetic behaviors and addressing frustration effects.

Contribution

It develops a symplectic N approach that explicitly incorporates time reversal symmetry, improving the modeling of frustrated magnetic systems.

Findings

Restores frustration dependence of critical spin in Neel phase

Accurately models finite temperature Ising transition

Incorporates energy costs of frustrated bonds

Abstract

Identifying the time reversal symmetry of spins as a symplectic symmetry, we develop a large N approximation for quantum magnetism that embraces both antiferromagnetism and ferromagnetism. In SU(N), N>2, not all spins invert under time reversal, so we have introduced a new large N treatment which builds interactions exclusively out of the symplectic subgroup [SP(N)] of time reversing spins, a more stringent condition than the symplectic symmetry of previous SP(N) large N treatments. As a result, we obtain a mean field theory that incorporates the energy cost of frustrated bonds. When applied to the frustrated square lattice, the ferromagnetic bonds restore the frustration dependence of the critical spin in the Neel phase, and recover the correct frustration dependence of the finite temperature Ising transition.