Incommensurate correlations in the anisotropic triangular Heisenberg lattice

TL;DR

This study investigates incommensurate spin correlations in the anisotropic triangular Heisenberg lattice, revealing persistent incommensurability across a broad parameter range and detailing how the wave vector approaches commensurate values as interchain coupling decreases.

Contribution

It provides a detailed numerical analysis of incommensurate correlations in the anisotropic triangular lattice using DMRG, highlighting their persistence and the behavior of the incommensurate wave vector.

Findings

Incommensurate correlations persist for all finite J'/J < Jc'/J.

The incommensurate wave vector approaches the antiferromagnetic value rapidly as J'/J decreases.

Correlations remain incommensurate despite the decoupling limit.

Abstract

We study the anisotropic spin-half antiferromagnetic triangular Heisenberg lattice in two dimensions, seen as a set of chains with couplings J (J') along (in between) chains, respectively. Our focus is on the incommensurate correlation that emerges in this system in a wide parameter range due to the intrinsic frustration of the spins. We study this system with traditional DMRG using cylindrical boundary conditions to least constrain possible incommensurate order. Despite that the limit of essentially decoupled chains J'/J < 0.5 is not very accessible numerically, it appears that the spin-spin correlations remain incommensurate for any finite 0 < J' < Jc', where Jc'/J > 1. The incommensurate wave vector q_J, however, approaches the commensurate value corresponding to the antiferromagnetic correlation of a single chain very rapidly with decreasing J'/J, roughly as q_J ~ pi - c_1 (J'/J)^n exp(-c_2 J/J').