Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9607171

Grand Canonical Partition Function for Unidimensional Systems: Application to Hubbard Model up to Order beta^3

I. C. Charret, S. M. de Souza, M. T. Thomaz, E. V. Correa Silva

Published Jul 24, 1996• 0 citations
arXivHTMLPDF

Abstract

We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co-factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order β^3, of the expansion of the grand canonical partition function for the Hubbard model in d=(1+1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.

DOI
10.48550/arxiv.cond-mat/9607171

Related papers

Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order $β^5$

I. C. Charret, E. V. Correa Silva, S. M. de Souza +1 more

We calculate the exact analytical coefficients of the $β$ expansion of the grand-canonical partition function of the unidimensional Hubbard model up to order $β^5$, using an alternative method, based on properties of the Grassmann algebra. The results derived are non-perturbative and no restrictions on the set of parameters that characterize the model are required. By applying this method we obtain analytical results for the thermodynamical quantities, in the high-temeprature limit, for arbitrary density of electrons in the unidimensional chain.

arXiv:cond-mat/9705241•May 23, 1997•0 citations

Grassmann algebra and fermions at finite temperature

I. C. Charret, E. V. Corrêa Silva, S. M. de Souza +2 more

For any d-dimensional self-interacting fermionic model, all coefficients in the high-temperature expansion of its grand canonical partition function can be put in terms of multivariable Grassmann integrals. A new approach to calculate such coefficients, based on direct exploitation of the Grassmannian nature of fermionic operators, is presented. We apply the method to the soluble Hatsugai–Kohmoto model, reobtaining well-known results.

arXiv:cond-mat/9809274•Journal of Mathematical Physics•Oct 1, 1999•3 citations

Grassmann Algebra and Fermions at Finite Temperature

I. C. Charret, E. V. Corrêa Silva, S. M. de Souza +4 more

For any d-dimensional self–interacting fermionic model, all coefficients in the high–temperature expansion of its grand canonical partition function can be put in terms of multivariable Grassmann integrals. A new approach to calculate such coefficients, based on direct exploitation of the grassmannian nature of fermionic operators, is presented. We apply the method to the soluble Hatsugai-Kohmoto model, reobtaining well-known results. PACS numbers: 02.90.+p, 05.30.Fk

•Jan 1, 1998•3 citations

Multivariable Grassmann integrals and the high temperature expansion of interacting fermionic models

I. C. Charret, E.V. Corrêa Silva, S. M. de Souza +1 more

Using the noncommuting nature of fermionic fields we obtain a nonperturbative method to calculate the high temperature limit of the grand canonical partition function of interacting fermionic models. This nonperturbative approach is applied to the Hubbard model in d=2(1+1) and we recover the known results in the limit T → ∞.

Journal of Mathematical Physics•Aug 1, 1995•2 citations

Functional approach without path integrals to finite temperature free fermions

S. M. de Souza, O. Rojas Santos, M. T. Thomaz

Charret et al. applied the properties of Grassmann generators to develop a new method to calculate the coefficientes of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models on d-dimensions (d > or = 1). The method explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. We apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the beta-independent and mu-independent infinities that plague the continuum path integral formulation.

Brazilian Journal of Physics•Sep 1, 1999•0 citations

Analytical results of the one-dimensional Hubbard model in the high-temperature limit

I. C. Charret, E. V. Corrêa Silva, S. M. de Souza +3 more

We investigate the grand potential of the one-dimensional Hubbard model in the high-temperature limit, calculating the coefficients of the high-temperature expansion $(\ensuremath{\beta}$-expansion) of this function up to order ${\ensuremath{\beta}}^{4}$ by an alternative method. The results derived are analytical and do not involve any perturbation expansion in the hopping constant, being valid for arbitrary density of electrons in the one-dimensional model. In the half-filled case, we compare our analytical results for the specific heat and the magnetic susceptibility, in the high-temperature limit, with the ones obtained by Beni et al. [Phys. Rev. B 8, 3329 (1973)] and Takahashi's integral equations, showing that the latter result does not take into account the complete energy spectrum of the one-dimensional Hubbard model. The exact integral solution by J\"uttner et al. [Nucl. Phys. B 522, 471 (1998)] is applied to the determination of the range of validity of our expansion in $\ensuremath{\beta}$ in the half-filled case, for several different values of U.

arXiv:cond-mat/9910043•Physical review. B, Condensed matter•Oct 29, 2001•6 citations
We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co-factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order β^3, of the expansion of the grand canonical partition function for the Hubbard model in d=(1+1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.
Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order β5β^5β5
We calculate the exact analytical coefficients of the βββ expansion of the grand-canonical partition function of the unidimensional Hubbard model up to order β5β^5β5, using an alternative method, based on properties of the Grassmann algebra. The results derived are non-perturbative and no restrictions on the set of parameters that characterize the model are required. By applying this method we obtain analytical results for the thermodynamical quantities, in the high-temeprature limit, for arbitrary density of electrons in the unidimensional chain.
Charret et al. applied the properties of Grassmann generators to develop a new method to calculate the coefficientes of the high temperature expansion of the grand canonical partition function of self-interacting fermionic models on d-dimensions (d > or = 1). The method explores the anti-commuting nature of fermionic fields and avoids the calculation of the fermionic path integral. We apply this new method to the relativistic free Dirac fermions and recover the known results in the literature without the beta-independent and mu-independent infinities that plague the continuum path integral formulation.
We investigate the grand potential of the one-dimensional Hubbard model in the high-temperature limit, calculating the coefficients of the high-temperature expansion $(\ensuremath{\beta}$-expansion) of this function up to order ${\ensuremath{\beta}}^{4}$ by an alternative method. The results derived are analytical and do not involve any perturbation expansion in the hopping constant, being valid for arbitrary density of electrons in the one-dimensional model. In the half-filled case, we compare our analytical results for the specific heat and the magnetic susceptibility, in the high-temperature limit, with the ones obtained by Beni et al. [Phys. Rev. B 8, 3329 (1973)] and Takahashi's integral equations, showing that the latter result does not take into account the complete energy spectrum of the one-dimensional Hubbard model. The exact integral solution by J\"uttner et al. [Nucl. Phys. B 522, 471 (1998)] is applied to the determination of the range of validity of our expansion in $\ensuremath{\beta}$ in the half-filled case, for several different values of U.