We formulate in terms of the quantum inverse scattering method the algebraic Bethe ansatz solution of the one-dimensional Hubbard model. The method developed is based on a new set of commutation relations which encodes a hidden symmetry of 6-vertex type.

In this paper we apply the anholonomic frames method developed in refs. [1–4] to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off–diagonal 5D metric, parameterized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting Einstein field equations. These simplified equations contain an interesting f...

This paper carries out the integration of Burgers equation by the aid of tanh method. This leads to the complex solutions for the Burgers equation, KdV–Burgers equation, coupled Burgers equation and the generalized time-delayed Burgers equation. Finally, the perturbed Burgers equation in (1+1) dimensions is integrated by the ansatz method. 2010 Elsevier Inc. All rights reserved.

We propose to boost the performance of density matrix renormalization group (DMRG) in two dimensions by using Gutzwiller projected states as initialization ansatz. When state is properly chosen, notorious "local minimum" issue DMRG can be circumvented and precision improved orders magnitude without extra computational cost. Moreover, this method allows quantify closeness initial final converged...

Motivated by Heilmann and Lieb’s work [8], we discuss energy level crossings for the one-dimensional Hubbard model through the Bethe ansatz, constructing explicitly the degenerate eigenstates at the crossing points. After showing the existence of solutions for the Lieb–Wu equations with one-down spin, we solve them numerically and construct Bethe ansatz eigenstates. We thus verify all the level...

Some features of integrable lattice models are reviewed for the case of the six-vertex model. By the Bethe ansatz method we derive the free energy of the six-vertex model. Then, from the expression of the free energy we show analytically the critical singularity near the phase transition in the anti-ferroelectric regime, where the essential singularity similar to the Kosterlitz-Thouless transit...