Phase diagram for a class of spin-half Heisenberg models interpolating between the square-lattice, the triangular-lattice and the linear chain limits

TL;DR

This paper maps out the phase diagram of a spin-half Heisenberg model interpolating between square, triangular, and chain limits, revealing complex magnetic phases influenced by frustration and quantum effects.

Contribution

It provides the first comprehensive phase diagram for this interpolating model using series expansions around multiple ground states.

Findings

Identification of multiple magnetic phases including Neel and 3-sublattice order.

Discovery of incommensurate magnetic order influenced by quantum fluctuations.

Evidence of nearly critical behavior in weakly coupled chain regime.

Abstract

We study the spin-half Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square-lattice at one end, a set of decoupled spin-chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations and varying dimensionality. There is a large region of the usual 2-sublattice Ne\'el phase, a 3-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wavevector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical.