Sign-problem-free effective models of spin-1/2 Heisenberg antiferromagnetism on the triangular lattice

A long-standing problem in the study of frustrated magnetism is an ubiquitous sign problem which often prevents large-scale numerical studies via Monte Carlo sampling. We present an effective lattice model of triangular lattice antiferromagnetism, using a Schwinger boson representation, that captures phases with 120° magnetic order, spin liquid phases, and valence bond solid (VBS) ordering. This is a theory of bosonic spinons on a triangular lattice coupled to an odd Z2 gauge field. A Berry phase term connected to the half-integer spin introduces a sign problem and naively renders the problem inaccessible through Monte Carlo techniques. Through a series of exact transformations, we derive a sign-problem-free representation of this model. Numerical results are presented which shed light on the nature of the critical theories separating the various phases in this model; in particular, the transition between 120° magnetic order and VBS order is analyzed.