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arXiv:cond-mat/9911141

Bosonization Based on Bethe Ansatz Equations and Spin-Charge Separation in the Hubbard Model with Finite U

Yue Yu, Huan-Xiong Yang, Yong-Shi Wu

Published Nov 10, 1999• 1 citation
arXivHTMLPDF

Abstract

We develop a bosonization approach for one-dimensional models based on Bethe ansatz equations. The operator formalism of the exact soluble models in the low energy limit provides a systematic method to calculate the asymptotic correlation functions. As examples with and without internal degrees of freedom, the Calogero-Sutherland (C-S) model and the repulsive Hubbard model are considered respectively. We verify that the low energy behavior of the C-S model is controlled by two classes of c=1 conformal field theories, depending on whether the C-S interactions are among bosons or among fermions. For the Hubbard model, we show the explicit charge-spin separation at low energy for arbitrary U>0. The low energy behavior of the system is described by the (semi-) direct product of two independent Virasoro algebras with c=1.

DOI
10.48550/arxiv.cond-mat/9911141

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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.
We investigate the low-temperature thermodynamics and correlation functions of one-dimensional spin-1/2 fermions with strong repulsion in an external magnetic field via the thermodynamic Bethe ansatz method. The exact thermodynamics of the model in a weak magnetic field is derived with the help of Wiener-Hopf techniques. It turns out that the low-energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(2)\text{SU}(2)SU(2) Heisenberg spin chain. However, these two types of conformally invariant low-lying excitations may break down as excitations take place far away from the Fermi points. The long distance asymptotics of the correlation functions and the critical exponents for the model in the presence of a magnetic field at zero temperature are derived in detail by solving dressed charge equations and by conformal mapping. Furthermore, we calculate the conformal dimensions for particular cases of correlation functions. The leading terms of these correlation functions are given explicitly for a weak magnetic field $H\ensuremath{\ll}1$ and for a magnetic field close to the critical field $H\ensuremath{\rightarrow}{H}_{c}$. Our analytical results provide insights into universal thermodynamics and criticality in one-dimensional many-body physics.
We consider a model of one-dimensional spin-1 bosons with repulsive density–density interactions and antiferromagnetic exchange. We show that the low energy effective field theory is given by a spin–charge separated theory of a Tomonaga–Luttinger Hamiltonian and the O(3) non-linear sigma model describing collective charge and spin excitations respectively. At a particular ratio of the density–density to spin–spin interaction the model is integrable, and we use the exact solutions to provide an independent derivation of the low energy effective theory. The system is in a superfluid phase made of singlet pairs of bosons, and we calculate the long-distance asymptotics of certain correlation functions.
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