From "Weak" to "Strong" Hole Confinement in a Mott Insulator

TL;DR

This paper investigates how a single hole behaves in 1D and 2D antiferromagnets, revealing a transition from weak to strong confinement due to string effects and magnon interactions.

Contribution

It provides an analytical comparison of hole confinement in 1D and 2D antiferromagnets, highlighting the role of string potentials and magnon interactions.

Findings

1D hole confinement is weak with exponential decay of magnon coefficients.

2D hole confinement is strong with superexponential decay, indicating string formation.

Magnon-magnon interactions are crucial in 1D for the confinement behavior.

Abstract

We study the problem of a single hole in an Ising antiferromagnet and, using the magnon expansion and analytical methods, determine the expansion coefficients of its wave function in the magnon basis. In the 1D case, the hole is "weakly" confined in a potential well and the magnon coefficients decay exponentially in the absence of a string potential. This behavior is in sharp contrast to the 2D square plane where the hole is "strongly" confined by a string potential and the magnon coefficients decay superexponentially. The latter is identified here to be a fingerprint of the strings in doped antiferromagnets that can be recognized in the numerical or cold atom simulations of the 2D doped Hubbard model. Finally, we attribute the differences between the 1D and 2D cases to the magnon-magnon interactions being crucially important in a 1D spin system.