5 research outputs found
Existence of Solutions to the Bethe Ansatz Equations for the 1D Hubbard Model: Finite Lattice and Thermodynamic Limit
In this work, we present a proof of the existence of real and ordered
solutions to the generalized Bethe Ansatz equations for the one dimensional
Hubbard model on a finite lattice, with periodic boundary conditions. The
existence of a continuous set of solutions extending from any positive U to the
limit of large interaction is also shown. This continuity property, when
combined with the proof that the wavefunction obtained with the generalized
Bethe Ansatz is normalizable, is relevant to the question of whether or not the
solution gives us the ground state of the finite system, as suggested by Lieb
and Wu. Lastly, for the absolute ground state at half-filling, we show that the
solution converges to a distribution in the thermodynamic limit. This limit
distribution satisfies the integral equations that led to the well known
solution of the 1D Hubbard model.Comment: 18 page
Lower bound for the segregation energy in the Falicov-Kimball model
In this work, a lower bound for the ground state energy of the
Falicov-Kimball model for intermediate densities is derived. The explicit
derivation is important in the proof of the conjecture of segregation of the
two kinds of fermions in the Falicov-Kimball model, for sufficiently large
interactions. This bound is given by a bulk term, plus a term proportional to
the boundary of the region devoid of classical particles. A detailed proof is
presented for density n=1/2, where the coefficient 10^(-13) is obtained for the
boundary term, in two dimensions. With suitable modifications the method can
also be used to obtain a coefficient for all densities.Comment: 8 pages, 2 figure