Eur. Phys. J. B (2013) 86: 408
https://doi.org/10.1140/epjb/e2013-40527-y

Regular Article

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

¹ Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno, 84084 Fisciano, Italy
² Unità CNISM di Salerno, Università degli Studi di Salerno, 84084 Fisciano, Italy
³ Istituto Internazionale per gli Alti Studi Scientifici (IIASS), 84019 Vietri sul Mare, Italy
⁴ Consiglio Nazionale delle Ricerche (CNR-SPIN), 67100 L’ Aquila, Italy
⁵ Department of Physics, Loughborough University, Loughborough LE11 3TU, UK

^a e-mail: plekhanoff@physics.unisa.it

Received: 27 May 2013
Received in final form: 2 August 2013
Published online: 1 October 2013

Abstract

We present the exact solution, obtained by means of the Transfer Matrix (TM) method, of the 1D Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) Coulomb interactions in the atomic limit (t = 0). The competition among the interactions (U, V₁, and V₂) generates a plethora of T = 0 phases in the whole range of fillings. U, V₁, and V₂ are the intensities of the local, NN and NNN interactions, respectively. We report the T = 0 phase diagram, in which the phases are classified according to the behavior of the principal correlation functions, and reconstruct a representative electronic configuration for each phase. In order to do that, we make an analytic limit T → 0 in the transfer matrix, which allows us to obtain analytic expressions for the ground state energies even for extended transfer matrices. Such an extension of the standard TM technique can be easily applied to a wide class of 1D models with the interaction range beyond NN distance, allowing for a complete determination of the T = 0 phase diagrams.