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 lattice 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.
Highlights
A Derivation of the formulae for the probabilities {Pn} A.1 1D with α = 1 A.2 1D with α < 1 A.3 2D with α ≤ 1
The central object that is calculated in this paper is the probability distribution {Pn} of observing n magnons in the wave function of a hole doped into the Ising antiferromagnet
In this paper we investigated in detail the particle localization in a Mott insulator that takes place when a single hole effectively moves in a confining potential
Summary
A tendency towards particle delocalization is an ubiquitous phenomenon in quantum mechanics, for it is encoded in the Heisenberg uncertainty principle for momentum and position operators [1]. The Mott localization is still not fully-understood and is an area of active research—both for an integer filling [5,6,7,8,9], as well as in doped systems [10,11,12,13,14,15,16,17,18,19,20] This lack of a complete understanding of the problem is largely due to the fact that the most widelyused models describing the problem (e.g. two-dimensional (2D) Hubbard [21], t–J [22, 23] or even the t–Jz [4] models) cannot be solved exactly [3] and the wave function of an electron in a Mott insulator is not known in general. Gether, this means that lowering dimensionality and adding interactions may remove “strong confinement” in favor of “weak confinement” in a strongly correlated system
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