Revisiting two holes in a locally antiferromagnetic background: the role of retardation and Coulomb repulsion effects

TL;DR

This paper investigates the behavior of two holes in an antiferromagnetic background using computational methods, revealing effects of retardation and Coulomb repulsion on hole pairing, distribution, and spin states in the t-J model.

Contribution

It demonstrates the significance of retardation effects and Coulomb repulsion in the two-hole problem, providing new insights into hole pairing and spin states in the t-J model.

Findings

Holes tend to be found at a distance of sqrt(2) lattice units, despite symmetry considerations.

Retardation effects lead to low-energy hole states with nonzero momentum and spin one.

Short-range Coulomb repulsion diminishes the relevance of very close hole-hole distances.

Abstract

The problem of two holes in the presence of strong antiferromagnetic fluctuations is revisited using computational techniques. Two-dimensional clusters and 2-leg ladders with up to 32 sites are studied with the Lanczos and Truncated Lanczos algorithms. The main motivation is the recently discussed spatial distribution of holes in ladders where the maximum probability for the hole-hole distance is obtained at d=sqrt(2) in units of the lattice spacing, a counter-intuitive result considering that the overall symmetry of the two-hole bound state is d_{x^2 - y^2}. The existence of holes in the same sublattice is argued to be a consequence of non-negligible retardation effects in the t-J model. The existence of strong spin singlets in the region where the two hole bound state is located is here confirmed, and a simple explanation for its origin in the case of planes is proposed. It is predicted that they should appear regardless of the long distance properties of the spin system under consideration, as long as the bound state is d_{x^2 - y^2}. In particular, it is shown that they are present in an Ising spin background. The time retardation in the family of t-J models leads naturally to low-energy hole states with nonzero momentum and spin one, providing a possible explanation for apparent SO(5)-symmetric features observed recently in this context. Finally, the influence of a short-range Coulombic repulsion is analyzed. The hole distribution in the d_{x^2 - y^2} bound state is reanalyzed in the presence of such repulsion. Very short hole-hole distances lose their relevance in the presence of a realistic hole-hole interaction.