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

  • Ferdinando Mancini
  • Evgeny PlekhanovEmail author
  • Gerardo Sica
Regular Article

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, V 1, and V 2) generates a plethora of T = 0 phases in the whole range of fillings. U, V 1, and V 2 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.

Keywords

Solid State and Materials 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ferdinando Mancini
    • 1
    • 2
    • 3
  • Evgeny Plekhanov
    • 4
    Email author
  • Gerardo Sica
    • 1
    • 5
  1. 1.Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di SalernoFiscianoItaly
  2. 2.Unità CNISM di Salerno, Università degli Studi di SalernoFiscianoItaly
  3. 3.Istituto Internazionale per gli Alti Studi Scientifici (IIASS)Vietri sul MareItaly
  4. 4.Consiglio Nazionale delle Ricerche (CNR-SPIN) L’AquilaItaly
  5. 5.Department of PhysicsLoughborough UniversityLoughboroughUK

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