Binding of holes and pair spectral function in the t-J model

TL;DR

This study investigates hole pairing and spectral functions in the two-dimensional t-J model, revealing a finite critical J for binding and suggesting a persistent quasiparticle weight proportional to J in the bulk limit.

Contribution

It provides numerical evidence for a critical J value for hole binding and analyzes the spectral function of d-wave pairs in the t-J model.

Findings

Binding energy indicates a finite critical J for bulk binding.

Finite overlap of d-wave pair operator with ground state for all clusters.

Quasiparticle weight likely remains finite and proportional to J in the bulk.

Abstract

Clusters of the two-dimensionnal t--J model with 2 holes and up to 26 sites are diagonalized using a Lanczos algorithm. The behaviour of the binding energy with system size suggests the existence of a finite critical value of J above which binding occurs in the bulk. Only the d-wave pair field operator acting on the Heisenberg GS has a finite overlap with the 2 hole ground state for all the clusters considered. The related spectral function associated with the propagation of a d-wave (spin singlet) pair of holes in the antiferromagnetic background is calculated. The quasiparticle peak at the bottom of the spectrum as well as some structure appearing above the peak survive with increasing cluster size. Although no simple scaling law was found for the quasiparticle weight the data strongly suggest that this weight is finite in the bulk limit and is roughly proportional to the antiferromagnetic coupling J (for J<1).