The method of evaluating quantum partition function for the Hubbard model

We present a technique for a numerical analysis of the phase structure of the two-dimensional Hubbard model as a function of the hole chemical potential. The grand-canonical partition function for the model is obtained via Monte Carlo simulations. The dependence of the hole occupation number on the chemical potential and the temperature is evaluated. These calculations, together with a study of the Yang-Lee zeros of the grand-canonical partition function, show evidence of a phase transition at zero temperature and particle density below half filling. The binding energy of a pair of holes is calculated in the low-temperature regime and the possibility for pairing is explored.We present a technique for a numerical analysis of the phase structure of the two-dimensional Hubbard model as a function of the hole chemical potential. The grand-canonical partition function for the model is obtained via Monte Carlo simulations. The dependence of the hole occupation number on the chemical potential and the temperature is evaluated. These calculations, together with a study of the Yang-Lee zeros of the grand-canonical partition function, show evidence of a phase transition at zero temperature and particle density below half filling. The binding energy of a pair of holes is calculated in the low-temperature regime and the possibility for pairing is explored.

arXiv:hep-lat/9205024Physical review. B, Condensed matterJul 1, 19926 citations

Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order $β^5$ 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.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/9705241May 23, 19970 citations

Analytical Results for the Grand-Canonical Partition Function for Unidimensional Hubbard Model up to Order

β^5

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.