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Journal of Physics A Mathematical and Theoretical

One-particle equal time correlation function for the spin-incoherent infiniteUHubbard chain

Vadim Cheianov, Mikhail B. Zvonarev

Published Jan 15, 2008• 4 citations
Publisher

Abstract

We present a calculation of the one-particle equal time correlation function.(x) for the one-dimensional (1D) Hubbard model in the infinite U limit. We consider the zero temperature spin incoherent regime, which is obtained by first taking the limit U --> infinity and then the limit T --> 0. Using the determinant representation for.(x), we derive analytical expressions for both large and small x at an arbitrary filling factor 0 < rho < 1/ 2. The large x asymptotics of rho(x) is found to be remarkably accurate starting from x sin(2 pi rho) similar to 1. We find that the one-particle momentum distribution function rho(k) is a smooth function of k, and. rho'(k) is peaked at k = 2k(F) in contrast to spin-coherent liquid obeying the Luttinger theorem.

DOI
10.1088/1751-8113/41/4/045002

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We present simple derivation of the Luttinger liquid relation for the 1D Hubbard model both for finite UUU and in the U=∞U=\inftyU=∞ limit. We describe the simple solution of the Hubbard model in the infinite repulsion limit and use it to calculate the correlators of the model in this limit in a simple and a physical way using the Bosonization technique. We then calculate the asymptotics of the correlators of the model at arbitrary UUU through the single parameter, which can be calculated from the Bethe Ansatz solution. Our derivation of the critical exponents is simple and allows one to express different physical operators of the Hubbard model through the charge and spin Bose fields in a direct and a physically transparent way.
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