Two-hole problem in the t-J model: A canonical transformation approach

TL;DR

This paper derives an effective Hamiltonian for quasiparticles in the t-J model using a canonical transformation, revealing a d-wave bound state relevant to superconductivity.

Contribution

It introduces a simple canonical transformation approach to account for hole interactions with spin waves and solves the two-hole bound state problem.

Findings

A d-wave bound state exists for 1< t/J <5.

The effective Hamiltonian closely matches self-consistent Born approximation results.

Both short-range and long-range spin-wave interactions influence pairing.

Abstract

The t-J model in the spinless-fermion representation is studied. An effective Hamiltonian for the quasiparticles is derived using canonical transformation approach. It is shown that the rather simple form of the transformation generator allows to take into account effect of hole interaction with the short-range spin waves and to describe the single-hole groundstate. Obtained results are very close to ones of the self-consistent Born approximation. Further accounting for the long-range spin-wave interaction is possible on the perturbative basis. Both spin-wave exchange and an effective interaction due to minimization of the number of broken antiferromagnetic bonds are included in the effective quasiparticle interaction. Two-hole bound state problem is solved using Bethe-Salpeter equation. The only d-wave bound state is found to exist in the region of 1< (t/J) <5. Combined effect of the pairing interactions of both types is important to its formation. Discussion of the possible relation of the obtained results to the problem of superconductivity in real systems is presented.