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Physical review. B, Condensed matter

Exact and numerical study of the effective hopping of a particle interacting with a fermionic bath in one dimension

X. Zotos, Frank Pelzer

Published Apr 1, 1988• 8 citations
Publisher

Abstract

We present an exact solution for the effective hopping of a particle interacting with spinless fermions of the same mass using the Bethe-ansatz method. We extend the study to interacting fermions by a numerical study on finite-size lattices and discuss its range of validity. We demonstrate the correspondence of the Bethe-ansatz collective excitation to the particle motion.

DOI
10.1103/physrevb.37.5045

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We present an exact solution for the effective hopping of a particle interacting with spinless fermions of the same mass using the Bethe-ansatz method. We extend the study to interacting fermions by a numerical study on finite-size lattices and discuss its range of validity. We demonstrate the correspondence of the Bethe-ansatz collective excitation to the particle motion.
One parametric one-dimensional spinless fermion model is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many-particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interaction. The ground-state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.
One parametric one-dimensional spinless fermion models is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian contains the kinetic terms describing nearest-neighbor hopping of electrons with different hopping integrals for many particle configurations. The Luttinger liquid behavior is studied for the case repulsion effective interactions. The ground state energy, the critical exponent, describing the asymptotic behavior of the density-density correlation function at long distances, the Fermi velocity have been calculated numerically for an arbitrary density of electrons. The model displays the condensation of particles in the case of the attractive interaction.
We calculate the asymptotics of correlation functions for the one-dimensional model of fermions with correlated hopping recently proposed by the author. The method of calculation is based on predictions of conformal field theory, the Bethe ansatz solutions, and a finite-size analysis of the gapless excitations. The critical exponents are given in terms of dressed charge matrix. Components of this matrix are solutions of a set of integral equations obtained from the Bethe ansatz. The effective transport mass is calculated for an arbitrary band filling.
A generalization of the $t\ensuremath{-}J$ model with a nearest-neighbor hopping is formulated and solved exactly by the Bethe ansatz method. The model describes the dynamics of spin-SSS fermions with isotropic or anisotropic interactions. In the case S=1S=1S=1 the magnetic interaction is biquadratic in the spin operators. In contrast to the SU(N)\mathrm{SU}(N)SU(N) generalization of the $t\ensuremath{-}J$ model, studied previously in the literature, the present model possesses beyond a massless excitation also a massive one. The physical properties indicate the existence of Cooper-type pairs with finite binding energy.
By the Bethe ansatz method we study the energy dispersion of a particle interacting by a local interaction with fermions (or hard core bosons) of equal mass in a one-dimensional lattice. We focus on the period of the Bloch oscillations, which turns out to be related to the Fermi wavevector of the Fermi sea and in particular on how this dispersion emerges as a collective effect in the thermodynamic limit. We also discuss the adiabatic coherent collective response of the system to an applied field.