Classical ground states of spin lattices

TL;DR

This paper extends the Luttinger-Tisza-Lyons-Kaplan theory to non-Bravais lattices, enabling the analysis of complex classical ground states including spin liquids and incommensurable states.

Contribution

It introduces a generalized method for determining classical ground states of non-Bravais lattices with Heisenberg interactions, expanding the applicability of existing theories.

Findings

Identified exclusive three-dimensional ground states in a modified honeycomb lattice.

Discovered classical spin-liquid ground states for certain coupling parameters.

Obtained incommensurable ground states in a modified square lattice.

Abstract

We present a generalization of the Luttinger-Tisza-Lyons-Kaplan (LTLK) theory of classical ground states of Bravais lattices with Heisenberg coupling to non-Bravais lattices. It consists of adding certain Lagrange parameters to the diagonal of the Fourier transformed coupling matrix analogous to the theory of the general ground state problem already published. This approach is illustrated by an application to a modified honeycomb lattice, which has exclusive three-dimensional ground states as well as a classical spin-liquid ground state for different values of the two coupling constants. Another example, the modified square lattice, shows that we can also obtain so-called incommensurable ground states by our method.