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Modern Physics Letters B

BOSONIZATION OF TWO-DIMENSIONAL HUBBARD MODEL

Yu-Liang Liu, Zhao-Bin Su

Published Oct 10, 1993• 0 citations
Publisher

Abstract

By analyzing one-dimensional (1D) chains arranged into a two-dimensional (2D) mesh and considering electrons tunneling from chain to chain at the intersection points, we use the 1D bosonization methods to describe the 2D Hubbard model, and find that the 2D Hubbard model can be completely represented by the spin and charge fields. It may provide evidence for spin and charge separation in some 2D quantum systems.

DOI
10.1142/s0217984993001545

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By analyzing one-dimensional (1D) chains arranged into a two-dimensional (2D) mesh and considering electrons tunneling from chain to chain at the intersection points, we use the 1D bosonization methods to describe the 2D Hubbard model, and find that the 2D Hubbard model can be completely represented by the spin and charge fields. It may provide evidence for spin and charge separation in some 2D quantum systems.
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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.
One of the central issues in the study of high-temperature superconducting cuprates which are composed of two-dimensional (2D) CuO 2 planes is whether the 2D systems with strong electron correlation behave as a Fermi liquid or a non-Fermi-liquid-like one-dimensional (1D) system with electron correlation. In this article, we start with the detailed examination of the electronic structure in cuprates and study theoretically the spin and charge dynamics in 1D and 2D cuprates. The theoretical background of spin-charge separation in the 1D model systems including the Hubbard and t - J models is presented. The first direct observation of collective modes of spin and charge excitations in a 1D cuprate, which are called spinons and holons respectively, in angle-resolved photoemission spectroscopy (ARPES) experiments is reviewed in the light of the theoretical results based on the numerically exact-diagonalization method. The charge and spin dynamics in 1D insulating cuprates is also discussed in connection with the spin-charge separation. The arguments are extended to the 2D cuprates, and the unique aspects of the electronic properties of high-temperature superconductors are discussed. Special emphasis is placed on the d-wave-like excitations in insulating 2D cuprates observed in ARPES experiments. We explain how the excitations are caused by the spin-charge separation. The charge stripes observed in the underdoped cuprates are examined in connection with spin-charge separation in real space.
This chapter explains bosonization, a useful technique for describing the low-energy properties of one-dimensional systems. Bosonization is introduced by presenting a model on which this method is essentially exact. This allows for the derivation of precise formulas that can be used for other models as well. Bosons are mapped with fermions and the effect of the interactions is examined. A one-dimensional system with spin is also discussed, and renormalization equations for sine-Gordon Hamiltonians are presented and analyzed. Furthermore, the generic phase diagram of a one-dimensional chain is obtained.