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arXiv:hep-th/9801167 · Physics Letters A

Temperature correlators in the one-dimensional Hubbard model in the strong coupling limit

A.G Izergin, A.G Pronko, N.I Abarenkova

Published Aug 1, 1998• 33 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(98)00442-3

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We consider the one-dimensional Hubbard model with the infinitely strong repulsion. The two-point dynamical temperature correlation functions are calculated. They are represented as Fredholm determinants of linear integrable integral operators. 1 Introduction The one-dimensional Hubbard model [1] is one of the most interesting and important model of strongly correlated electrons (see, e.g., book [2]). The hamiltonian of the model with the chemical potential h in the external constant field B describes interacting fermions on the one-dimensional periodic lattice of length L: HU = \\Gamma L X x=1 X ff=";# i c y x;ff c x\\Gamma1;ff + c y x\\Gamma1;ff c x;ff j +h L X x=1 (n x;" + n x;# ) \\Gamma B L X x=1 (n x;" \\Gamma n x;# ) + U L X x=1 n x;" n x;# : (1) Here c x;ff and c y x;ff (x = 1; . . . ; L; ff ="; #; c 0;ff j c L;ff ; c y 0;ff j c y L;ff ) are canonical fermion fields with the anticommutation relations [c x;ff ; c y y;fi ] + = ffi x;y ffi ff;fi ...
Correlations of a one-dimensional doubly degenerate Hubbard model are studied for the one-quarter-filled case. Exact calculations on a four-site lattice show that a ferromagnetic state exists in the strong-coupling regime. For a one-dimensional chain, a strong-coupling effective Hamiltonian was studied using a self-consistent calculation, a high-temperature expansion, and quantum Monte Carlo simulations. The results provide information on the parameters needed for ferromagnetic correlations, and the temperature dependence of the spin and orbital correlations.
The ``string'' structure of one-dimensional Hubbard model eigenstates is studied numerically and is used to suggest the validity of thermodynamic Bethe-ansatz equations (TBAE). We furthermore solve TBAE in a strong-coupling expansion series form and obtain the thermodynamic potential which agrees with the known high-temperature expansion series. We also calculate various thermodynamic quantities using our solution and provide some additional features of the strongly correlated one-dimensional Hubbard model.