Nonextensive thermodynamics of the two-site Hubbard model

Abstract

Thermodynamical properties of canonical and grand-canonical ensembles of the half-filled two-site Hubbard model have been discussed within the framework of the nonextensive statistics (NES). For relating the physical temperature $T$ to the Lagrange multiplier $\beta$, two methods have been adopted: $T=1/k_B\beta$ in the method A [Tsallis {\it et al.} Physica A {\bf 261} (1998) 534], and $T=c_q/k_B\beta$ in the method B [Abe {\it et al.} Phys. Lett. A {\bf 281} (2001) 126], where $k_B$ denotes the Boltzman constant, $c_q={\sum }_i{p}_i^q$, $p_i$ the probability distribution of the $i$th state, and $q$ the entropic index. Temperature dependences of specific heat and magnetic susceptibility have been calculated for $1 \lleq q \lleq 2$, the conventional Boltzman-Gibbs statistics being recovered in the limit of $q=1$. The Curie constant ${\Gamma }_q$ of the susceptibility in the atomic and low-temperature limits ($t/U\to 0,T/U\to 0$) is shown to be given by ${\Gamma }_q=2q{2}^{2(q-1)}$ in the method A, and ${\Gamma }_q=2q$ in the method B, where $t$ stands for electron hoppings and $U$ intra-atomic interaction in the Hubbard model. These expressions for ${\Gamma }_q$ are shown to agree with the results of a free spin model which has been studied also by the NES with the methods A and B. A comparison has been made between the results for canonical and grand-canonical ensembles of the model.

arXiv comment22 pages, 7 figures, accepted in Physica A with minor changes

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• Specific heat and entropy of $N$-body nonextensive systems
• Hubbard pair cluster in the external fields. Studies of the magnetic properties
• Thermal entanglement of Hubbard dimers in the nonextensive statistics
• Hubbard pair cluster with elastic interactions. Studies of thermal expansion, magnetostriction and electrostriction
• Nonextensive quantum method for itinerant-electron ferromagnetism: Fractorization approach
• The entropy in finite $N$-unit nonextensive systems: the ordinary average and $q$-average
• Full self-consistency versus quasiparticle self-consistency in diagrammatic approaches: Exactly solvable two-site Hubbard Model