Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit

摘要

We present the exact solution, obtained by means of the Transfer Matrix (TM)method, of the 1D Hubbard model with nearest-neighbor (NN) andnext-nearest-neighbor (NNN) Coulomb interactions in the atomic limit (t=0). Thecompetition among the interactions ($U$, $V_1$, and $V_2$) generates a plethoraof T=0 phases in the whole range of fillings. $U$, $V_1$, and $V_2$ are theintensities of the local, NN and NNN interactions, respectively. We report theT=0 phase diagram, in which the phases are classified according to the behaviorof the principal correlation functions, and reconstruct a representativeelectronic configuration for each phase. In order to do that, we make ananalytic limit $T\to 0$ in the transfer matrix, which allows us to obtainanalytic expressions for the ground state energies even for extended transfermatrices. Such an extension of the standard TM technique can be easily appliedto a wide class of 1D models with the interaction range beyond NN distance,allowing for a complete determination of the T=0 phase diagrams.