The interplay and competition of magnetic and superconducting correlations in the weakly interacting two-dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of interactions in one-loop approximation evolves into a strong coupling regime at low energy scales, signalling the possible onset of spontaneous symmetry breaking. This is further analyzed by a mean-field treatment of the strong renormalized interactions which takes into account magnetic and superconducting order simultaneously. The effect of strong correlations on single-particle properties in the normal phase is studied by calculating the flow of the self-energy. 1The interplay and competition of magnetic and superconducting correlations in the weakly interacting two-dimensional Hubbard Model is investigated by means of the functional renormalization group. At zero temperature the flow of interactions in one-loop approximation evolves into a strong coupling regime at low energy scales, signalling the possible onset of spontaneous symmetry breaking. This is further analyzed by a mean-field treatment of the strong renormalized interactions which takes into account magnetic and superconducting order simultaneously. The effect of strong correlations on single-particle properties in the normal phase is studied by calculating the flow of the self-energy. 1

Jan 1, 200610 citations

Magnetism and superconductivity within extended Hubbard model for a dimer. Exact results

B. Grabiec, S. Krawiec, M. Matlak

We find the eigenvalues $E_α $ and eigenvectors $|E_α>$ of the extended Hubbard dimer and we represent each part $E_α |E_α> < E_α |$ of the dimer Hamiltonian $(α=1,2,...,16)$ in the second quantizations with the use of the Hubbard and spin operators. This procedure gives a review of all competitive, intrinsic interactions, deeply hidden in the orginal form of the considered Hamiltonian. Among competitive interactions we can find ferromagnetic and antiferromagnetic interactions (also in the form appearing in the $t-J$ model), hopping of the Cooper pairs between different dimer lattice sites (similar as in Kulik-Pedan, Penson-Kolb models), as well as, intersite Cooper pair interactions. We plot several coupling constants of these interactions vs Coulomb intrasite interaction $U$ to show that the competition between them strongly depends on the model parameters. The thermodynamical activity of each particular interaction, belonging to a given energy level, depends, however, on the occupation of this level. From the presented review of interactions it is evident that the extended Hubbard model is capable to describe the properties of superconductors with magnetic ordering (including also high- $T_C$ superconductors) where a strong competition between magnetism and superconductivity takes place.We find the eigenvalues $E_α $ and eigenvectors $|E_α>$ of the extended Hubbard dimer and we represent each part $E_α |E_α> < E_α |$ of the dimer Hamiltonian $(α=1,2,...,16)$in the second quantizations with the use of the Hubbard and spin operators. This procedure gives a review of all competitive, intrinsic interactions, deeply hidden in the orginal form of the considered Hamiltonian. Among competitive interactions we can find ferromagnetic and antiferromagnetic interactions (also in the form appearing in the $t-J$ model), hopping of the Cooper pairs between different dimer lattice sites (similar as in Kulik-Pedan, Penson-Kolb models), as well as, intersite Cooper pair interactions. We plot several coupling constants of these interactions vs Coulomb intrasite interaction $U$ to show that the competition between them strongly depends on the model parameters. The thermodynamical activity of each particular interaction, belonging to a given energy level, depends, however, on the occupation of this level. From the presented review of interactions it is evident that the extended Hubbard model is capable to describe the properties of superconductors with magnetic ordering (including also high-$T_C$ superconductors) where a strong competition between magnetism and superconductivity takes place.

arXiv:cond-mat/0511329Nov 14, 20052 citations

Thermodynamic and transport properties of infinite U Hubbard model

Rishabh Kishore, A K Mishra

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.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.

Journal of Physics Conference SeriesJan 1, 20100 citations

Magnetic Interactions in the Hubbard Model.

P. M. Mihas

Jan 1, 19770 citations

We find the eigenvalues $E_α $ and eigenvectors

|E_α>

of the extended Hubbard dimer and we represent each part

E_α |E_α> < E_α |

of the dimer Hamiltonian

(α=1,2,...,16)

in the second quantizations with the use of the Hubbard and spin operators. This procedure gives a review of all competitive, intrinsic interactions, deeply hidden in the orginal form of the considered Hamiltonian. Among competitive interactions we can find ferromagnetic and antiferromagnetic interactions (also in the form appearing in the

t-J

model), hopping of the Cooper pairs between different dimer lattice sites (similar as in Kulik-Pedan, Penson-Kolb models), as well as, intersite Cooper pair interactions. We plot several coupling constants of these interactions vs Coulomb intrasite interaction

U

to show that the competition between them strongly depends on the model parameters. The thermodynamical activity of each particular interaction, belonging to a given energy level, depends, however, on the occupation of this level. From the presented review of interactions it is evident that the extended Hubbard model is capable to describe the properties of superconductors with magnetic ordering (including also high-

T_C

superconductors) where a strong competition between magnetism and superconductivity takes place.