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Generic Hubbard Hamiltonian for 1D Large-Spin Ultracold Fermionic Chains

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Abstract

A new version of the generalized Hubbard Hamiltonian is introduced here for high-spin ultracold fermions, which was used to study a spin-5/2 fermionic lattice numerically. The number of states in the energy multiplets agrees with the dimensions of low-order irreducible representations (IRs) for the symmetries expected. Furthermore, the exact diagonalization (ED) technique and the nearest-neighbor Casimir-Casimir correlations were employed to investigate numerically the quantum-phase transitions of 1D ultracold spin-3/2 fermionic lattices. With these IRs it was possible to explain the appearance of the symmetries in 1D ultracold spin-3/2 fermionic chains at quarter filling (one particle per site) and for repulsive interactions. Young’s diagrams were used to explain graphically the absence of exchange interactions for the SU(4) model. It is relevant that the generalized Hubbard Hamiltonian could be used to compute the hidden symmetries and reduce the problem complexity.

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Acknowledgements

The author acknowledges the financial support from the Brazilian Agency FAPESP (process no. 2017/25587-5), and the support from CIBioFi and the Colombian Science, Technology and Innovation Foundation COLCIENCIAS Francisco José de Caldas under project 1106-712-49884 (contract no. 264-2016) and General Royalties System (Fondo CTeI-SGR) under contract no. BPIN 2013000100007. He is also grateful to Prof. Osvaldo N. Oliveira Jr from University of Sao Paulo for proof-reading the manuscript.

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  1. Sao Carlos Institute of Physics, University of Sao Paulo, 13560-970, Sao Carlos, 369, Sao Paulo, Brazil

    J. J. Hernández-Sarria

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Hernández-Sarria, J.J. Generic Hubbard Hamiltonian for 1D Large-Spin Ultracold Fermionic Chains. J Supercond Nov Magn 34, 3431–3439 (2021). https://doi.org/10.1007/s10948-021-06057-9

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