Strong Coupling Limit and Some Exact Results

Luigi Accardi, A. Frigerio, Yun Gang Lu

P. R. Vansant, M. A. Smondyrev, François Maria Peeters +1 more

Equations for the bipolaron wavefunction, ground-state energy and effective mass are derived which are exact in the strong-coupling limit. The results are obtained for large bipolarons in an arbitrary number of spatial dimensions (D). We apply our results to the cases D=1,2,3.

D. M. Esterling

Exact spectral moment relations are derived and presented for the low temperature, strong coupling limit of the Hubbard model, for any dimension, lattice structure and electron density. These results generate an exact, rigorous and quantitative test for proposed solutions to the Hubbard model that claim to be valid in the strong coupling, low temperature region. The test complements analyses for weak coupling and high temperatures, offering insights into the essential physics of the model, specifically the quasiparticle energy (centroid) and lifetime (width) of the spectral weight function in the infinite coupling, finite hopping limit. Numerical results are given for nearest neighbour hopping in 1, 2 and 3D.

F. Benatti, Roberto Floreanini B

Eva Kalinowski, Władysław Gluza

The ground-state energy of the Hubbard model on a Bethe lattice with infinite connectivity at half filling is calculated for the insulating phase. Using Kohn's transformation to derive an effective Hamiltonian for the strong-coupling limit, the resulting class of diagrams is determined. We develop an algorithm for an algebraic evaluation of the contributions of high-order terms and check it by applying it to the Falicov-Kimball model that is exactly solvable. For the Hubbard model, the ground-state energy is exactly calculated up to order ${t}^{12}/{U}^{11}$. The results of the strong-coupling expansion deviate from numerical calculations as quantum Monte Carlo (or density-matrix renormalization group) by less than $0.13%$ ($0.32%$ respectively) for $U>4.76$.

J. Galán, José Antonio Vergés