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Magnetic and superconducting competition within the Hubbard dimer. Exact solution
Author(s) -
Matlak M.,
Słomska T.,
Grabiec B.
Publication year - 2005
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200460051
Subject(s) - hubbard model , hamiltonian (control theory) , antiferromagnetism , dimer , physics , superconductivity , condensed matter physics , coupling constant , ferromagnetism , quantum mechanics , mathematical physics , mathematics , nuclear magnetic resonance , mathematical optimization
We express the Hubbard dimer Hamiltonian $ H_{d} = {\textstyle \sum \nolimits ^{16} _{\alpha = 1} }E_{\alpha}\vert E_{\alpha}\rangle \langle E_{\alpha}\vert $ in the second quantization with theuse of the Hubbard and spin operators. We consider the case of positive and negative U . We decompose the resulting Hamiltonian into several parts collecting all the terms belonging to the same energy level. Such a decomposition visualizes explicitely all intrinsic interactions competing together and deeply hidden in the original form of the dimer Hamiltonian. Among them are competitive ferromagnetic and antiferromagnetic interactions. There are also hopping terms present which describe Cooper pairs hopping between sites 1 and 2 with positive and negative coupling constants (similar as in Kulik–Pedan, Penson–Kolb models). We show that the competition between intrinsic interactions strongly depends on the model parametrs and the averaged occupation number of electrons n ∈ [0, 4] resulting in different regimes of the model (as e.g. t – J model regime, etc.). (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)