An Exact Diagonalization Study of the Anisotropic Triangular Lattice Heisenberg Model Using Twisted Boundary Conditions

TL;DR

This study uses twisted boundary conditions and exact diagonalization to analyze the phase diagram of the anisotropic triangular Heisenberg model, revealing a phase transition between incommensurate spiral order and short-range correlations.

Contribution

It introduces a novel application of twisted boundary conditions with exact diagonalization to accurately determine phase boundaries in a challenging incommensurate system.

Findings

Identification of a phase transition between spiral and short-range phases.

Close agreement with DMRG results on larger systems.

Evidence of near-degenerate antiferromagnetic and ferromagnetic correlations.

Abstract

The anisotropic triangular model, which is believed to describe the materials Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$, among others, is dominated by incommensurate spiral physics and is thus extremely resistant to numerical analysis on small system sizes. In this paper we use twisted boundary conditions and exact diagonalization techniques to study the phase diagram of this model. With these boundary conditions we are able to extract the inter- and intrachain ordering $q$-vectors for the $\frac{J'}{J} < 1$ region finding very close agreement with recent DMRG results on much larger systems. Our results suggest a phase transition between a long-range incommensurate spiral ordered phase, and a more subtle phase with short-range spiral correlations with the $q$-vector describing the incommensurate correlations varying smoothly through the transition. In the latter phase correlations between next-nearest chains exhibits an extremely close competition between predominantly antiferromagnetic and ferromagnetic correlations. Further analysis suggests that the antiferromagnetic next-nearest chain correlations may be slightly stronger than the ferromagnetic ones. This difference is found to be slight but in line with previous renormalization group predictions of a collinear antiferromagnetic ordering in this region.