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arXiv:cond-mat/9504122 · Journal of the Physical Society of Japan

Spin-Charge Separation at Finite Temperature in the Supersymmetrict-JModel with Long-Range Interactions

Yoshio Kuramoto, Yusuke S. Kato

Published Dec 15, 1995• 30 citations
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Abstract

Thermodynamics is derived rigorously for the 1D supersymmetric {\it t-J} model and its SU($K,1$) 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($K,1$) model are ascribed to free para-fermions of order $K-1$.

DOI
10.1143/jpsj.64.4518

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Dynamical Properties of the 1/r2-Type Supersymmetrict-JModel in a Magnetic Field: Manifestation of Spin-Charge Separation

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The dynamical spin structure factor S zz ( Q , ω) in the small momentum region is derived analytically for the one-dimensional supersymmetric t – J model with 1/ r 2 interaction. Strong spin–charge separation is found in the spin dynamics. The structure factor S zz ( Q , ω) with a given spin polarization does not depend on electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S zz ( Q , ω). These results are derived via solution of the SU (2,1) Sutherland model in the strong coupling limit.

arXiv:cond-mat/0607444•Journal of Physics A Mathematical and General•Aug 9, 2006•8 citations
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.
We construct thermodynamics of the one-dimensional supersymmetric t-J model with the 1/sin 2 interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component t-J model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.
We construct thermodynamics of the one-dimensional supersymmetric {\it t-J} model with the $ 1/\sin^2$ interaction and hopping. The thermodynamics is described exactly in terms of free spinons and holons obeying Haldane's fractional exclusion statistics at all temperatures. Moreover, at low temperatures the semionic spinons and holons decouple resulting in the spin-charge separation in thermodynamic properties. We obtain explicit results for the spin and charge susceptibilities and specific heat, and interpret them in terms of the fractional exclusion statistics. Extension to the multi-component {\it t-J} model shows that the excitations obey either fractional statistics for g-ons with partial polarization of components, or the parafermionic one without polarization.
Quasi-particle picture in a magnetic field is pursued for dynamical spin and charge correlation functions of the one-dimensional supersymmetric t-J model with inverse-square interaction. With use of exact diagonalization and the asymptotic Bethe-ansatz equations for finite systems, excitation contents of relevant excited states are identified which are valid in the thermodynamic limit. The excitation contents are composed of spinons, antispinons, holons and antiholons obeying fractional statistics. Both longitudinal and transverse components of the dynamical spin structure factor are independent of the electron density in the region where only quasi-particles with spin degrees of freedom (spinons and antispinons) contribute. The dynamical charge structure factor does not depend on the spin-polarization density in the region where only quasi-particles with charge (holons and antiholons) are excited. These features indicate the strong spin-charge separation in dynamics, reflecting the high symmetry of the model.
Dynamical charge structure factor N(Q,ω)N(Q,ω)N(Q,ω) with QQQ smaller than the Fermi wave number is derived analytically for the one-dimensional supersymmetric t-J model with 1/r21/r^21/r2 interaction. Strong spin-charge separation in dynamics is found. N(Q,ω)N(Q,ω)N(Q,ω) with given electron density does not depend on the spin polarization for arbitrary size of the system. In the thermodynamic limit, only two holons and one antiholon contribute to N(Q,ω)N(Q,ω)N(Q,ω). These results together with generalized ones for the SU(KKK,1) supersymmetric t-J model are derived via solution of the Sutherland model in the strong coupling limit.
Abstract We analyze the thermodynamics and the critical behavior of the supersymmetric t - J model with long-range interactions. Using the transfer matrix formalism, we obtain a closed-form expression for the free energy per site both for a finite number of sites and in the thermodynamic limit. Our approach, which is different from the usual ones based on the asymptotic Bethe ansatz and generalized exclusion statistics, can in fact be applied to a large class of models whose spectrum is described in terms of supersymmetric Young tableaux and their associated Haldane motifs. In the simplest and most interesting case, we identify the five ground state phases of the model and derive the complete low-temperature asymptotic series of the free energy per site, the magnetization and charge densities, and their susceptibilities. We verify the model’s characteristic spin-charge separation at low temperatures, and show that it holds to all orders in the asymptotic expansion. Using the low-temperature asymptotic expansions of the free energy, we also analyze the critical behavior of the model in each of its ground state phases. While the standard phase is described by two independent conformal field theories (CFTs) with central charge c = 1 in correspondence with the spin and charge sectors, we find that the low-energy behavior of the and phases is that of a single c = 1 CFT. We show that the model exhibits an even richer behavior on the boundary between zero-temperature phases, where it can be non-critical but gapless, critical in the spin sector but not in the charge one, or critical with central charge c = 3/2.
The dynamical spin structure factor S zz ( Q , ω) in the small momentum region is derived analytically for the one-dimensional supersymmetric t – J model with 1/ r 2 interaction. Strong spin–charge separation is found in the spin dynamics. The structure factor S zz ( Q , ω) with a given spin polarization does not depend on electron density in the small momentum region. In the thermodynamic limit, only two spinons and one antispinon (magnon) contribute to S zz ( Q , ω). These results are derived via solution of the SU (2,1) Sutherland model in the strong coupling limit.