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

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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.

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Authors and Affiliations

  1. Dipartimento di Fisica “E.R. Caianiello”, Università degli Studi di Salerno, 84084, Fisciano, Italy

    Ferdinando Mancini & Gerardo Sica

  2. Unità CNISM di Salerno, Università degli Studi di Salerno, 84084, Fisciano, Italy

    Ferdinando Mancini

  3. Istituto Internazionale per gli Alti Studi Scientifici (IIASS), 84019, Vietri sul Mare, Italy

    Ferdinando Mancini

  4. Consiglio Nazionale delle Ricerche (CNR-SPIN), 67100, L’Aquila, Italy

    Evgeny Plekhanov

  5. Department of Physics, Loughborough University, Loughborough, LE11 3TU, UK

    Gerardo Sica

Authors
  1. Ferdinando Mancini
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  2. Evgeny Plekhanov
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  3. Gerardo Sica
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Correspondence to Evgeny Plekhanov.

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Mancini, F., Plekhanov, E. & Sica, G. Exact solution of the 1D Hubbard model with NN and NNN interactions in the narrow-band limit. Eur. Phys. J. B 86, 408 (2013). https://doi.org/10.1140/epjb/e2013-40527-y

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  • DOI: https://doi.org/10.1140/epjb/e2013-40527-y

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