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Physica B Condensed Matter

Thermodynamic properties of the one-dimensional supersymmetric t−J model at finite temperatures

Sei-ichiro Suga, Ayao Okiji

Published Jul 1, 1997• 3 citations
Publisher
DOI
10.1016/s0921-4526(97)00057-4

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arXiv:cond-mat/9601132•Jan 27, 1996•0 citations
A Trotter-Suzuki mapping is used to calculate the finite-temperature properties of the one-dimensional supersymmetric t − J model. This approach allows for the exact calculation of various thermodynamical properties by means of the quantum transfer matrix (QTM). The free energy and other interesting quantities are obtained such as the specific heat and compressibility. For the largest eigenvalue of the QTM leading to the free energy a set of just two non-linear integral equations is presented. These equations are studied analytically and numerically for different particle densities and temperatures. The structure of the specific heat is discussed in terms of the elementary charge as well as spin excitations. Special emphasis is placed on the study of the low-temperature behavior confirming scaling predictions by conformal field theory and Luttinger liquid theory. To our knowledge this is the first complete investigation of a strongly correlated electron system on a lattice at finite temperature.
Abstract This work is dedicated to the study of a supersymmetric quantum spherical spin system with short-range interactions. We examine the critical properties both a zero and finite temperature. The model undergoes a quantum phase transition at zero temperature without breaking supersymmetry. At finite temperature the supersymmetry is broken and the system exhibits a thermal phase transition. We determine the critical dimensions and compute critical exponents. In particular, we find that the model is characterized by a dynamical critical exponent z = 2. We also investigate properties of correlations in the one-dimensional lattice. Finally, we explore the connection with a nonrelativistic version of the supersymmetric nonlinear sigma model and show that it is equivalent to the system of spherical spins in the large N limit.
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.