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Different Approximations for Hubbard Model

Jerzy Mizia, Grzegorz Górski

Elsevier eBooksJan 1, 20070 citations

Influence of spin-wave excitations on the ferromagnetic phase diagram in the Hubbard model

W. Rumsch, Wolfgang Nolting

The subject of the present paper is the theoretical description of collective electronic excitations, i.e., spin waves, in the Hubbard model. Starting with the widely used random-phase approximation, which combines Hartree-Fock theory with the summation of the two-particle ladder, we extend the theory to a more sophisticated single particle approximation, namely, the spectral-density ansatz. Doing so we have to introduce a ``screened'' Coulomb interaction rather than the bare Hubbard interaction in order to obtain physically reasonable spinwave dispersions. The discussion following the technical procedure shows that comparison of standard RPA with our new approximation reduces the occurrence of a ferromagnetic phase further with respect to the phase diagrams delivered by the single particle theories.The subject of the present paper is the theoretical description of collective electronic excitations, i.e., spin waves, in the Hubbard model. Starting with the widely used random-phase approximation, which combines Hartree-Fock theory with the summation of the two-particle ladder, we extend the theory to a more sophisticated single particle approximation, namely, the spectral-density ansatz. Doing so we have to introduce a ``screened'' Coulomb interaction rather than the bare Hubbard interaction in order to obtain physically reasonable spinwave dispersions. The discussion following the technical procedure shows that comparison of standard RPA with our new approximation reduces the occurrence of a ferromagnetic phase further with respect to the phase diagrams delivered by the single particle theories.

arXiv:cond-mat/0209480Physical review. B, Condensed matterNov 25, 20027 citations

Spin susceptibilities for the Hubbard model in a band approach

Alexander A. Ovchinnikov, M. Ya. Ovchinnikova

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2 D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω ( Q )= c | Q −(π, π)| near Q ∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X ″( Q,ω →0) gives the same mode with a peak at Q ∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X ″( Q,ω →0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector.The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2 D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω ( Q )= c | Q −(π, π)| near Q ∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X ″( Q,ω →0) gives the same mode with a peak at Q ∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X ″( Q,ω →0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector.

Journal of Experimental and Theoretical PhysicsSep 1, 19990 citations

Dynamical Vertex Approximation for the Hubbard Model

A. Toschi

Bulletin of the American Physical SocietyMar 18, 20160 citations

One-loop approximation for the Hubbard model

A. Sherman

Physica C SuperconductivityMar 29, 20070 citations

Collective-mode dispersion of atomic Fermi gases in a honeycomb optical lattice: Speed of sound of the attractive Kane–Mele–Hubbard model at half filling

Zlatko G. Koinov

We examine the superfluid states that emerge in the Kane–Mele model as a result of the on-site short-range attractive interaction U. The collective-mode dispersion is defined by the solutions of the Bethe–Salpeter (BS) equation in the generalized random phase approximation. The slope of the low-energy (Goldstone) mode and the corresponding sound velocity at half filling, calculated within the BS formalism, has been compared with the corresponding results obtained previously by the T-matrix approximation. The difference between the two approaches is that the T-matrix approximation takes into account only the ladder diagrams, and neglects the bubble ones. For this reason, the sound velocity in the direction toward point M, calculated within the T-matrix approximation, is about 4% less than the result obtained by employing the BS equation.We examine the superfluid states that emerge in the Kane–Mele model as a result of the on-site short-range attractive interaction U. The collective-mode dispersion is defined by the solutions of the Bethe–Salpeter (BS) equation in the generalized random phase approximation. The slope of the low-energy (Goldstone) mode and the corresponding sound velocity at half filling, calculated within the BS formalism, has been compared with the corresponding results obtained previously by the T-matrix approximation. The difference between the two approaches is that the T-matrix approximation takes into account only the ladder diagrams, and neglects the bubble ones. For this reason, the sound velocity in the direction toward point M, calculated within the T-matrix approximation, is about 4% less than the result obtained by employing the BS equation.

Low Temperature PhysicsMay 1, 20201 citation

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