Binding carriers to a non-magnetic impurity in a two-dimensional square Ising antiferromagnet

TL;DR

This paper studies how a quasiparticle in a 2D Ising antiferromagnet interacts with a non-magnetic impurity, revealing that magnon coupling can induce bound states even when the impurity and quasiparticle are on different sublattices.

Contribution

It demonstrates that magnon interactions create effective disorder leading to bound states, even when the impurity and quasiparticle are on different sublattices, extending understanding of impurity effects in Ising antiferromagnets.

Findings

Magnon coupling induces effective disorder on the quasiparticle's sublattice.

Bound states form even when the impurity and quasiparticle are on different sublattices.

The spectrum of bound states differs significantly depending on sublattice configuration.

Abstract

A hole in a two-dimensional Ising antiferromagnet was believed to be infinitely heavy due to the string of wrongly oriented spins it creates as it moves, which should trap it near its original location. Trugman showed that, in fact, the hole acquires a finite effective mass due to contributions from so-called {\it Trugman loop} processes, where the hole goes nearly twice around closed loops, first creating and then removing wrongly-oriented spins, and ending up at a different lattice site. This generates effective second- and third-nearest-neighbor hopping terms which keep the quasiparticle on the sublattice it was created on. Here, we investigate the trapping of the quasiparticle near a single attractive non-magnetic impurity placed at one lattice site. We consider the two cases with the quasiparticle and impurity being on the same versus on different sublattices. The main result is that even though the quasiparticle can not see the bare disorder in the latter case, the coupling to magnons generates an effective renormalized disorder on its own sublattice which is strong enough to lead to bound states, which however have a very different spectrum than when the quasiparticle and impurity are on the same sublattice.