Krzysztof Bieniasz, Piotr Wrzosek, Andrzej M. Oles, Krzysztof Wohlfeld
SciPost Phys. 7, 066 (2019) ·
published 27 November 2019
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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.
