Spin-Charge Separated Luttinger Liquid in Arbitrary Spatial Dimensions


A model with a singular forward scattering amplitude for particles with opposite spins in d spatial dimensions is proposed and solved by using the bosonization transformation. This interacting potential leads to the spincharge separation. Thermal properties at low temperature for this Luttinger liquid are discussed. Also, the explicit form of the single-electron Green function is found; it has square-root branch cut. New fermion field operators are defined; they describe holons and spinons as the elementary excitations. Their single particle Green functions possess pseudoparticle properties. Using these operators the spin-charge separated Hamiltonian for an ideal gases of holons and spinons is derived and reflects an inverse (fermionization) transformation. PACS Nos.71.10.+x, 71.27.+a Typeset using REVTEX ∗E-mail: byczuk@fuw.edu.pl, ufspalek@if.uj.edu.pl 1 It was suggested [1] that the properties of normal state of high-temperature superconductors are properly described by Luttinger liquid, where the spin and charge degrees of freedom are separated. In one-dimensional systems this phenomenon is well understood [2]. However, in two and three dimensions the present understanding of the spin-charge separation is rather poor. In this letter we formulate and solve exactly a d-dimensional model exhibiting the spin-charge separation, as well as discuss its thermal and dynamic properties. A natural approach to study spin-charge decoupling phenomena is the bosonization transformation, generalized recently to the multidimensional space situation [3]. Here we adopt the operator version of the bosonization developed in Ref. [4]. The starting assumption in this method is the existence of the Fermi surface (FS) defined as a collection of points at which the momentum distribution function has singularities at zero temperature (T = 0). These points are parameterized by vectors S and T, which label a finite and a locally flat (rectangular in shape) mesh of grid points on FS with spacing Λ ≪ kF between them [4,3]. Introducing coarse-grained density fluctuation operators Jσ(S,q), defined in boxes centered at each FS point and having surface area Λd−1 and the thicknesses λ/2 both above and below it, one can transform the effective Hamiltonian for interacting fermions into an effective Hamiltonian for free bosons. Explicitly, it takes the general form H = 1 2 ∑

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@inproceedings{Byczuk1995SpinChargeSL, title={Spin-Charge Separated Luttinger Liquid in Arbitrary Spatial Dimensions}, author={Krzysztof Byczuk}, year={1995} }