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Revista Mexicana de Física

Repulsive bound-electron pairs in a Peierls lattice

Uriel Alberto Díaz-Reynoso, Ernesto Huipe-Domratcheva, Oracio Navarro

Published Sep 1, 2023• 1 citation
Publisher

Abstract

A new class of repulsive bound-electron pairs have been found in a Peierls lattice within the Hubbard model for energies E < 0 despite U > 0. These new repulsive bound-electron pairs have a high degree of localization as both the correlation energy U and the tS/tL hopping ratio increases. In order to study electronic correlation in Peierls lattices, our previous real space mapping method has also been extended to the so called generalized mapping method which is briefly presented here. In this paper, we concentrate our attention to discuss in detail the two-particle problem within a repulsive Hubbard model for the one-dimensional Peierls lattice.

DOI
10.31349/revmexfis.69.051601

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A new class of repulsive bound-electron pairs have been found in a Peierls lattice within the Hubbard model for energies E < 0 despite U > 0. These new repulsive bound-electron pairs have a high degree of localization as both the correlation energy U and the tS/tL hopping ratio increases. In order to study electronic correlation in Peierls lattices, our previous real space mapping method has also been extended to the so called generalized mapping method which is briefly presented here. In this paper, we concentrate our attention to discuss in detail the two-particle problem within a repulsive Hubbard model for the one-dimensional Peierls lattice.
In this work we solve a general Hubbard Hamiltonian for two interacting particles in a periodic and nonperiodic infinite one-dimensional lattice, using a real-space mapping method, the renormalized perturbation expansion (RPE), and the Green-function technique. This Hamiltonian considers a general bond-charge interaction, the on-site interaction, and the general intersite interaction. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding problem in a higher-dimensional space. Analyzing the periodic and the quasiperiodic lattices in this new space, we obtained the analytical solution for the binding condition at the ground state. Our general results for the periodic chain reproduce completely the limit cases of the numerical solution obtained previously and those obtained in reciprocal space
Motivated by aspects of layered high-temperature superconductors and related quasi-one-dimensional materials, we consider polaron structure, dynamics, and coherence in certain extended Peierls–Hubbard models. We emphasize the qualitative importance of electron–lattice interactions even in the presence of dominant electron–electron correlations, the signatures of polaron structure and dynamics in energy-resolved pair-distribution structure functions, and the effect of disorder on polaron propagation and stability. Introduction The formation and dynamics of polarons (and bipolarons), despite a halfcentury of theoretical and experimental study, remain fascinating topics in many-body physics, combining as they do (often competing) aspects of coupled fields with distinct natural time scales (e.g., electron–phonon, spin–phonon, exciton–phonon), electron–electron interactions, lattice discreteness, nonadiabaticity, collective quantum tunneling, thermal fluctuations, competitions between disorder and polaronic localization, etc. Direct observation of polarons through real-space imaging of any of the coupled fields is rare even with the advent of STEM , AFM techniques, etc. Likewise, global measurements such as that of electronic band-structure are insensitive to polaron features. Thus, experiments and theoretical techniques have had to focus on indirect effects on microscopic probes such as transport coefficients, electronic absorption, vibrational spectroscopy, and so forth. Our purpose here is to briefly review three qualitative effects in polaron physics that have arisen in modeling two components of the lattice structure of the layered cuprate superconductors [1] – namely, extended multi-band Peierls–Hubbard models of (a) the active CuO 2 planes and (b) polarizable Cu–O clusters in the axial direction (polarizable interplanar medium).
A detailed study of the behavior of two electrons in the square lattice is presented in which the dynamics of the electronic pair is described by the t-J model. The conditions for the formation of bound states, pair correlation functions, and the energy spectra are obtained. The analysis is extended to the Cooper problem, i.e., to the study of the wave function of two electrons above the filled Fermi sea. Finally, the quantitative relationship between the t-J model and the one-band Hubbard model is numerically investigated for the two-electron problem.
We study mesoscopic pairing in the one-dimensional repulsive Hubbard model and its interplay with the BCS model in the canonical ensemble. The key tool is comparing the Bethe ansatz equations of the two models in the limit of small Coulomb repulsion. For the ordinary Hubbard interaction the BCS Bethe equations with infinite pairing coupling are recovered; a finite pairing is obtained by considering a further density-dependent phase-correlation in the hopping amplitude of the Hubbard model. We find that spin degrees of freedom in the Hubbard ground state are arranged in a state of the BCS type, where the Cooper pairs form a noncondensed liquid on a ``lattice'' of single particle energies provided by the Hubbard charge degrees of freedom; the condensation in the BCS ground state corresponds to Hubbard excitations constituted by a sea of spin singlets.