Phase diagram of the spin-1 Heisenberg model with three-site interactions on the square lattice

TL;DR

This paper explores the complex phase diagram of a spin-1 Heisenberg model with three-site interactions on a square lattice, revealing a rich variety of magnetic and quadrupolar phases through analytical and numerical methods.

Contribution

It introduces and analyzes a spin-1 model with three-site interactions, uncovering a potentially seven-phase sequence and enriching understanding of frustrated quantum magnetic systems.

Findings

Identification of up to seven distinct phases as interaction ratios vary.

Discovery of phases with collinear magnetic order and mixed magnetic-quadrupolar order.

Demonstration of the model's high frustration and complex phase behavior.

Abstract

We study the spin S=1 antiferromagnetic Heisenberg model on the square lattice with, in addition to the nearest-neighbor interaction, a three-site interaction of the form (S_i S_j)*(S_j S_k) + h.c.. This interaction appears naturally in a strong coupling exansion of the two-orbital, half-filled Hubbard model. For spin 1/2, this model reduces to a Heisenberg model with bilinear interactions up to third neighbors, with a second-neighbor interaction twice as large the third-neighbor one, a very frustrated model with an infinite family of helical classical ground states in a large parameter range. Using a variety of analytical and numerical methods, we show that the spin-1 case is also very frustrated, and that its phase diagram is even richer, with possibly the succession of seven different phases as a function of the ratio of the three-site interaction to the bilinear one. The phases are either purely magnetic phases with collinear order, or of mixed magnetic and quadrupolar character with helical order.