A numerical and analytical study of two holes doped into the 2D t--J model

TL;DR

This paper combines numerical exact diagonalization and analytical methods to study two holes in the 2D t-J model, revealing a bound state with d_{x^2-y^2} symmetry and validating a quasiparticle description.

Contribution

It provides a detailed numerical and analytical analysis of hole pairing and quasiparticle behavior in the 2D t-J model, with new insights into the bound state symmetry.

Findings

Identification of a lowest energy bound state with d_{x^2-y^2} symmetry

Analytical agreement with numerical electron momentum distribution

Support for the quasiparticle Hamiltonian description

Abstract

Exact diagonalization numerical results are presented for a 32-site square cluster, with two holes propagating in an antiferromagnetic background described by the t-J model. We characterize the wave function of the lowest energy bound state found in this calculation, which has d_{x^2-y^2} symmetry. Analytical work is presented, based on a Lang-Firsov-type canonical transformation derived quasiparticle Hamiltonian, that accurately agrees with numerically determined values for the electron momentum distribution function and the pair correlation function. We interpret this agreement as strong support for the validity of this description of the hole quasiparticles.