Exact ground state and kink-like excitations of a two dimensional Heisenberg antiferromagnet

TL;DR

This paper introduces a two-dimensional Heisenberg antiferromagnet with an exact dimerized ground state, revealing unique kink-like excitations and a connection to one-dimensional spin chain phenomena.

Contribution

It presents a rare 2D Heisenberg model with an exact ground state and domain-wall-like excitations, bridging 1D and 2D quantum spin systems.

Findings

Exact dimerized ground state identified

Presence of kink-like excitations in 2D system

Decoupling into non-interacting chains in certain limits

Abstract

A rare example of a two dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it is probably the first genuinely two-dimensional quantum system to exhibit domain-wall-like ``kink'' excitations normally found only in one-dimensional systems. In some limits it decouples into non-interacting chains, purely dynamically and not because of weakening of interchain couplings: indeed, paradoxically, this happens in the limit of strong coupling of the chains.