Piotr Wrzosek, Adam Kłosiński, Yao Wang, Mona Berciu, Cliò Efthimia Agrapidis, Krzysztof Wohlfeld
SciPost Phys. 17, 018 (2024) ·
published 19 July 2024
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The stability of the spin polaron quasiparticle, well established in studies of a single hole in the 2D antiferromagnets, is investigated in the 1D antiferromagnets using a $t$-$J$ model. We perform an exact slave fermion transformation to the holon-magnon basis, and diagonalize numerically the resulting model in the presence of a single hole. We demonstrate that the spin polaron collapses - and the spin-charge separation takes over - due to the specific role played by the magnon-magnon interactions and the magnon hard-core constraint in the 1D $t$-$J$ model. Moreover, we prove that the spin polaron is stable for any strength of the magnon-magnon interaction other than the unique value found in a 1D antiferromagnet with the continuous symmetry of the spin interactions. Fine-tuning to this unique value is extremely unlikely to occur in quasi-1D antiferromagnets, therefore the spin polaron is the stable quasiparticle of realistic 1D materials. Our results lead to a new interpretation of the ARPES spectra of quasi-1D antiferromagnets in the spin polaron language.
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.
