We present an asymptotically exact solution of the infinite-dimensional Hubbard model at a special interaction strength ${\mathit{U}}_{\mathit{T}}$ corresponding to the strong-coupling Fermi-liquid fixed point. This solution is intimately related to the Toulouse limit of the single-impurity Kondo model and the symmetric Anderson model in its strong-coupling limit.We present an asymptotically exact solution of the infinite-dimensional Hubbard model at a special interaction strength ${\mathit{U}}_{\mathit{T}}$ corresponding to the strong-coupling Fermi-liquid fixed point. This solution is intimately related to the Toulouse limit of the single-impurity Kondo model and the symmetric Anderson model in its strong-coupling limit.

arXiv:cond-mat/9401023Physical review. B, Condensed matterMar 15, 19941 citation

Strong-coupling perturbation theory of the Hubbard model

S. Pairault, David Sénéchal, A.–M. S. Tremblay

arXiv:cond-mat/9905242The European Physical Journal BJun 1, 2000118 citations

Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model

Balázs Hetényi, Luís Miguel Martelo, B. Tanatar

We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model with focus on the strong-coupling regime via variational, exact diagonalization, and strong coupling calculations. Our variational approach is based on the Baeriswyl wave function, implemented via Monte Carlo sampling. We derive the superfluid weight appropriately in a variational setting. We emphasize the importance of implementing the Peierls phase in position space and to allow for many-body interference effects, rather than implementing the Peierls phase as single particle momentum shifts. At integer filling, the Baeriswyl wave function gives zero superfluid response at any coupling. At half filling our variational superfluid weight is in reasonable agreement with exact diagonalization results. We also calculate the polarization amplitude, the variance of the total position, and the associated size scaling exponent, which corroborate that this variational approach produces an insulating state at integer filling. Our Baeriswyl based variational method is applicable to significantly larger system sizes than exact diagonalization or quantum Monte Carlo.We calculate the superfluid weight and the polarization amplitude for the one-dimensional bosonic Hubbard model with focus on the strong-coupling regime via variational, exact diagonalization, and strong coupling calculations. Our variational approach is based on the Baeriswyl wave function, implemented via Monte Carlo sampling. We derive the superfluid weight appropriately in a variational setting. We emphasize the importance of implementing the Peierls phase in position space and to allow for many-body interference effects, rather than implementing the Peierls phase as single particle momentum shifts. At integer filling, the Baeriswyl wave function gives zero superfluid response at any coupling. At half filling our variational superfluid weight is in reasonable agreement with exact diagonalization results. We also calculate the polarization amplitude, the variance of the total position, and the associated size scaling exponent, which corroborate that this variational approach produces an insulating state at integer filling. Our Baeriswyl based variational method is applicable to significantly larger system sizes than exact diagonalization or quantum Monte Carlo.

arXiv:1909.06050Physical review. B./Physical review. BNov 25, 20192 citations

Variational Approach for the Bose-Hubbard Model

于得水, Jingbiao Chen

Chinese Physics LettersJan 1, 20080 citations

We present an asymptotically exact solution of the infinite-dimensional Hubbard model at a special interaction strength

{\mathit{U}}_{\mathit{T}}

corresponding to the strong-coupling Fermi-liquid fixed point. This solution is intimately related to the Toulouse limit of the single-impurity Kondo model and the symmetric Anderson model in its strong-coupling limit.