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Journal of the Physical Society of Japan

Generalized Gutzwiller States as Exact Excited States in the One-Dimensional Supersymmetrict-JModel with Long-Range Exchange and Transfer

Hisatoshi Yokoyama, Yoshio Kuramoto

Published Sep 15, 1992• 10 citations
Publisher

Abstract

A set of generalized Gutzwiller-type wave functions with spin and charge currents and/or spin polarization are shown to be exact eigenstates of the supersymmetric t - J -type model with long-range interactions. The increment of energy in the presence of currents is proportional to the square of the currents without any higher-order corrections for arbitrary size of the system. The exact excited states are identified by the absence of statistical fluctuations in the variational Monte Carlo calculation. The spin susceptibility is found to be independent of the size, as in the case of the charge susceptibility.

DOI
10.1143/jpsj.61.3046

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A set of generalized Gutzwiller-type wave functions with spin and charge currents and/or spin polarization are shown to be exact eigenstates of the supersymmetric t - J -type model with long-range interactions. The increment of energy in the presence of currents is proportional to the square of the currents without any higher-order corrections for arbitrary size of the system. The exact excited states are identified by the absence of statistical fluctuations in the variational Monte Carlo calculation. The spin susceptibility is found to be independent of the size, as in the case of the charge susceptibility.
The Gutzwiller wave function is shown to be the exact solution of a supersymmetric t-J-type model. The model realizes a Fermi-liquid state in one dimension with a discontinuity in the momentum distribution. Analytic results are obtained for spin and charge susceptibilities, and the specific-heat coefficient with the help of the Luttinger-liquid theory. In the high-density limit the model exhibits a Mott-Hubbard gap and reduces to an antiferromagnetic spin chain with long-range exchange solved by Haldane and Shastry.
The Gutzwiller wave function is shown to be the exact solution of a supersymmetric t-J-type model. The model realizes a Fermi-liquid state in one dimension with a discontinuity in the momentum distribution. Analytic results are obtained for spin and charge susceptibilities, and the specific-heat coefficient with the help of the Luttinger-liquid theory. In the high-density limit the model exhibits a Mott-Hubbard gap and reduces to an antiferromagnetic spin chain with long-range exchange solved by Haldane and Shastry.
Thermodynamics is derived rigorously for the 1D supersymmetric {\it t-J} model and its SU(K,1K,1K,1) generalization with inverse-square exchange. The system at low temperature is described in terms of spinons, antispinons, holons and antiholons obeying fractional statistics. They are all free and make the spin susceptibility independent of electron density, and the charge susceptibility independent of magnetization. Thermal spin excitations responsible for the entropy of the SU(K,1K,1K,1) model are ascribed to free para-fermions of order K−1K-1K−1.
Excitation spectra in the SU(ν+1ν+1ν+1,1) supersymmetric t-J model with long-range exchange and transfer has quadratic dependence on spin and charge currents for all energies. After brief review on the supersymmetry, this paper gives a simple explanation for the spin-charge separation on the basis of a first-quantized representation. A useful identity is derived on permutation properties of SU(ννν) Jastrow-type wave functions, which constitute the ground states for a class of 1/r2r^2r2 interaction models.
The dynamical properties of the one-dimensional supersymmetric t-J model in a magnetic field at T=0 are investigated within the framework of the one-dimensional Landau-liquid theory. The effect of the magnetic field on the low-energy excitation spectrum is analyzed. The transport properties of the t-J model are studied in the low-frequency long-wavelength regime. The effective charge and spin of the elementary carriers are evaluated from the spectral currents. A microscopic criterion for the separation of charge and spin degrees of freedom is established and it is shown that the charge-spin recombination across the ferromagnetic boundary is complete in the supersymmetric t-J model. The charge and spin stiffnesses are expressed in terms of the matrix elements of electronic charge and spin fluctuations between Bethe eigenstates.