Hole and Pair Structures in the t-J model

TL;DR

This study uses DMRG calculations to analyze hole and pair structures in the t-J model, revealing how holes bind in pairs within antiferromagnetic systems and identifying specific low-energy configurations at various doping levels.

Contribution

It provides a detailed numerical and theoretical analysis of hole pairing mechanisms and structures in the t-J model, especially in two-dimensional and ladder systems.

Findings

Holes tend to bind on 2x2 plaquettes with diagonal site preference.

Frustrating antiferromagnetic bonds facilitate hole pairing.

Additional low-energy structures include spin-liquid regions and 1D hole chains.

Abstract

Using numerical results from density matrix renormalization group (DMRG) calculations for the t-J model, on systems as large as 10x7, we examine the structure of the one and two hole ground states in ladder systems and in two dimensional clusters. A simple theoretical framework is used to explain why holes bind in pairs in two-dimensional antiferromagnets. For the case J/t=0.5, which we have studied, the hole pairs reside predominantly on a 2x2 core plaquette with the probability that the holes are on diagonal sites greater than nearest-neighbor sites. There is a strong singlet bond connecting the spins on the two remaining sites of the plaquette. We find that a general characteristic of dynamic holes in an antiferromagnet is the presence of frustrating antiferromagnetic bonds connecting next-nearest-neighbor sites across the holes. Pairs of holes bind in order to share the frustrating bonds. At low doping, in addition to hole pairs, there are two additional low-energy structures which spontaneously form on certain finite systems. The first is an undoped Lx2 spin-liquid region, or ladder. The second is a hole moving along a one dimensional chain of sites. At higher doping we expect that hole pairing is always favored.