Bound states of holes in an antiferromagnet

TL;DR

This study uses numerical methods to investigate hole bound states in an antiferromagnetic background, revealing a critical coupling for bound state formation with d-wave symmetry, relevant to high-temperature superconductor theories.

Contribution

It demonstrates the existence of two-hole bound states with d-wave symmetry in the t-J model above a critical coupling, providing insight into pairing mechanisms in cuprates.

Findings

Bound states form for J/t > J/t]_c

Bound states have dx2-y2 symmetry

Quasiparticle weight remains finite across couplings

Abstract

The formation of bound states of holes in an antiferromagnetic spin-1/2 background is studied using numerical techniques applied to the ${\rm t-J}$ Hamiltonian on clusters with up to 26 sites. An analysis of the binding energy as a function of cluster size suggests that a two hole bound state is formed for couplings larger than a ``critical'' value ${\rm J/t]_c}$. The symmetry of the bound state is $\dx2y2$. We also observed that its ``quasiparticle'' weight ${\rm Z_{2h}}$ (defined in the text), is finite for all values of the coupling ${\rm J/t}$. Thus, in the region ${\rm J/t \geq J/t]_c}$ the bound state of two holes behaves like a quasiparticle with charge $Q=2e$, spin $S=0$, and $\dx2y2$ internal symmetry. The relation with recent ideas that have suggested the possibility of d-wave pairing in the high temperature cuprate superconductors is briefly discussed.