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Journal of Physics Conference Series

Thermodynamic and transport properties of infinite U Hubbard model

Rishabh Kishore, A K Mishra

Published Jan 1, 2010• 0 citations
Publisher

Abstract

The infinite U Hubbard model, which excludes double occupancy of electrons on a lattice site, can be considered as an exactly solvable non-interacting orthofermion model. We obtained several thermodynamic and transport properties like specific heat, entropy, magnetization, magnetic susceptibility and thermoelectric power for the non-interacting orthofermions. It is found that in one dimension our results coincides with that of known exact results. In case of thermoelectric power, we have also obtained the generalized Heikes formula in high temperature limits and Stafford results at low temperatures. Since the non-interacting orthofermion model is exactly solvable in any dimension, our results can be used as a guide to ascertain the accuracy of the approximations, used to solve the finite U Hubbard model, frequently employed for the study of the strongly correlated electron systems.

DOI
10.1088/1742-6596/200/1/012085

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The infinite U Hubbard model, which excludes double occupancy of electrons on a lattice site, can be considered as an exactly solvable non-interacting orthofermion model. We obtained several thermodynamic and transport properties like specific heat, entropy, magnetization, magnetic susceptibility and thermoelectric power for the non-interacting orthofermions. It is found that in one dimension our results coincides with that of known exact results. In case of thermoelectric power, we have also obtained the generalized Heikes formula in high temperature limits and Stafford results at low temperatures. Since the non-interacting orthofermion model is exactly solvable in any dimension, our results can be used as a guide to ascertain the accuracy of the approximations, used to solve the finite U Hubbard model, frequently employed for the study of the strongly correlated electron systems.
Hubbard model plays a critical role in the study of strongly correlated electron systems. The only available exact solutions of 1-D Hubbard Hamiltonian, obtained through nested Bethe ansatz, show a spin charge decoupling for infinite U when there is no possibility of double occupancy of an electron orbital state. It had been shown that these features can be directly obtained by employing orthofermion algebra. In the present communication, the thermodynamic properties, namely, specific heat and entropy are provided for a 1-D chain and 2-D square lattice using orthofermion approach. It is shown that in 1-D, our results are identical to the known exact results. We have also compared the thermodynamic properties of free fermions and orthofermions in both 1-D and 2-D. Our thermodynamic results, based on orthofermion approach, can be used to ascertain the accuracy of the approximate methods employed in the context of infinite U Hubbard model.
In order to determine finite-temperature properties of the infinite one-dimensional Hubbard model for the half-filled band, finite systems such as chains with 2 to 5 atoms and rings with 4 and 6 atoms are studied with the application of the grand canonical ensemble. The obtained temperature dependence of the specific heat, the entropy, the magnetic susceptibility and some correlation functions clearly shows a rearrangement of the electronic state of the system with the increase of the strength of the Coulomb interaction relative to the transfer integral. In the light of our new results the functional integral approach recently proposed by Kimball and Schrieffer as well as Hubbard's approximate theory is examined.
The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0<q<π) into the state with strong antiferromagnetic correlations (q=π) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.
The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0<q<π) into the state with strong antiferromagnetic correlations (q=π) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.
[[abstract]]The phase diagram and thermodynamic properties of the Hubbard model in one dimension are calculated numerically within the generalized self-consistent approach over a wide range of temperature T, magnetic field h, interaction strength U/t and electron concentration n. The temperature variation of the transverse magnetization, double occupied sites and chemical potential at various n, U/t and h is also analyzed. The wave vector q for the magnetic order parameter in the vicinity of the half-filling in the metallic phase shows a crossover from incommensurate magnetic phase (0 < q < pi) into the state with strong antiferromagnetic correlations (q = pi) as temperature is increased. Overall our numerical results in the approximate theory at finite temperatures are in good quantitative and qualitative agreement with the Bethe-ansatz results.
In order to contribute to understand well the thermodynamic properties of strongly correlated electron systems, we study numerically, in the grand canonical ensemble, the temperature dependence of the internal energy, specific heat, entropy, magnetization, and magnetic susceptibility of the one-dimensional Hubbard model without transference of moment in the interactions. The results have been obtained for a wide range of values of the on-site Coulombian repulsion U and of the external magnetic field h. Differences between this model and the original Hubbard model have been observed in relation to the number of peaks of the specific heat and to the behavior of the susceptibility in temperatures tending to zero. These differences evidence that the two models possess different magnetic structures of correlation.