Beyond Schwinger boson mean-field theory: Numerical simulations of quantum and classical Heisenberg models

Schwinger boson “parton” constructions provide a systematic way to study frustrated quantum spin lattice Hamiltonians via bosonic formal methods without making limiting assumptions about the symmetries of the ground state. Despite this versatility, thermodynamic treatments are limited to mean-field and “large N” SU(N) approaches because of highly oscillatory statistical weights that render Monte Carlo methods inapplicable. Furthermore, Schwinger boson methods require careful treatment of constraints that faithfully map the bosonic Fock space to a spin-S subspace.



Here, we present progress in numerically sampling the Schwinger boson coherent-state path-integral representation of quantum Heisenberg models at finite temperature. We introduce a projected complex Langevin numerical technique that enforces the Schwinger boson constraints exactly at each sampling iteration, leading to improvements in the approach’s stability and efficiency. We apply our method to a S = 3/2 frustrated triangular antiferromagnet to demonstrate the technique’s access to equilibrium spin textures, spin-spin correlations, properties, and comparisons of quantum and classical effects. We conclude with a discussion of the current method’s limitations and potential applications.