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arXiv:0912.5386

Computer simulations for the extended Hubbard model utilizing Nonextensive Statistical Mechanics

J. F. V. Flores

Published Jan 1, 2011• 1 citation
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Abstract

We study a system formed by M dimers through half-filled two-site Hubbard model, with two electrons. Our approach use the third version of Nonextensive Statistical Mechanics as tool for calculating thermodynamic and magnetic parameters such as entropy, internal energy, magnetization and specific heat. In the computer simulations, we vary the q entropic index values between 1 and 2, such that, q = 1.0, 1.4, 1.7 and 2.0. These values are interesting to study small magnetic systems. We find the critical temperature regions in simulations with the simple Hubbard model, i.e. without the intersite interaction. For other side, adding this additional term, we notice an enlargement and shifting of the thermodynamic parameters comparing with the obtained from simple Hubbard model; even more, we found in some cases the absence of the critical temperature regions.

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We study a system formed by M dimers through half-filled two-site Hubbard model, with two electrons. Our approach use the third version of Nonextensive Statistical Mechanics as tool for calculating thermodynamic and magnetic parameters such as entropy, internal energy, magnetization and specific heat. In the computer simulations, we vary the q entropic index values between 1 and 2, such that, q = 1.0, 1.4, 1.7 and 2.0. These values are interesting to study small magnetic systems. We find the critical temperature regions in simulations with the simple Hubbard model, i.e. without the intersite interaction. For other side, adding this additional term, we notice an enlargement and shifting of the thermodynamic parameters comparing with the obtained from simple Hubbard model; even more, we found in some cases the absence of the critical temperature regions.
Abstract We hereby introduce a research about a grand canonical ensemble for the extended two-site Hubbard model, that is, we consider the intersite interaction term in addition to those of the simple Hubbard model. To calculate the thermodynamical parameters, we utilize the nonextensive statistical mechanics; specifically, we perform the simulations of magnetic internal energy, specific heat, susceptibility, and thermal mean value of the particle number operator. We found out that the addition of the intersite interaction term provokes a shifting in all the simulated curves. Furthermore, for some values of the on-site Coulombian potential, we realize that, near absolute zero, the consideration of a chemical potential varying with temperature causes a nonzero entropy. PACS 75.10.Jm, 05.30.-d, 65.80.+n
With the aim of contributing to a better understanding of the finite-temperature properties of low-dimensional strongly correlated systems we study a one-dimensional half-filled-band extended Hubbard model with a term of exchange interaction between neighboring sites. We analyze the temperature dependence of the specific heat, internal energy, entropy, number of doubly occupied sites, magnetic susceptibility, spin-spin correlation functions, and also investigate a detailed diagram of magnetic correlations. We use the method of small-cluster exact diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined model exhibits a rich structure of magnetic properties due to the competition between the onsite Coulombian repulsion and the exchange interaction.
A perturbation expansion for the thermodynamic potential is performed to the third order by HTSE method. Entropy, internal energy, specific heat, and magnetic susceptibility of the one-dimensional extended Hubbard model are computed as functions of temperature, electron density, and t, U, W. Thermodynamics can be discussed in two temperature regions. The high T-region corresponds to increase in number of double occupied states. The low T-region corresponds to the distribution of electron spin. The effect of t on thermodynamic properties is obvious.
The extended Hubbard model in the zero-bandwidth limit is studied.The eective Hamiltonian consists of (i) on-site U interaction, (ii) intersite densitydensity interaction W , and (iii) Ising-like magnetic exchange interaction J between the nearest-neighbors.We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D chain in two particular cases: (a) W = 0 and n = 1; (b) U → +∞ and n = 1/2 (W = 0, J = 0).We obtain the exact formulae for the partition functions which enables to calculate thermodynamic properties such as entropy, specic heat (c), and double occupancy per site.In both cases the system exhibits an interesting temperature dependence of c involving a characteristic two-peak structure.There are no phase transitions at nite temperatures and the only transitions occur in the ground state.
The dimerized-chain Hubbard model is characterized by a Coulomb energy UUU and two alternating transfer constants, an intradimer constant ttt, and a smaller interdimer constant ${t}^{\ensuremath{'}}$. We have used thermodynamic perturbation theory to treat the half-filled-band case, taking the interdimer transfer as the perturbation term. The unperturbed problem is a lattice of isolated dimers. We give the energy, specific heat, and magnetic susceptibility as functions of temperature for the unperturbed case and for the first nonvanishing order in the perturbation. The results are consistent with the U=0U=0U=0 case, which is solved exactly. The interdimer transfer ${t}^{\ensuremath{'}}$ has the effect of distorting the peaks in the specific heat and reducing the susceptibility; this is shown graphically.
A new first-principles method for numerically calculating finite-temperature properties of quantum many-body systems is described. It is used to compute the thermodynamic properties and magnetic correlations of the Hubbard model, with negligible error at temperatures near the bandwidth or above. Results for the half-filled band and a simple cubic or one-dimensional lattice confirm the existence of a high-temperature peak in the specific heat which has been associated with a smooth but rapid change in conductivity. Correlations calculated for the non-half-filled band simple cubic Hubbard model suggest condensation, an entirely unexpected phenomenon whose existence is shown (by unrelated methods) in Paper II.