The Thermodynamic Properties of Some Integrable Systems.
Abstract
I discuss the thermodynamic properties of integrable quantum systems, in particular, generalizations of the Heisenberg chain and the onedimensional Hubbard model, by making use of the BetheAnsatz technique. For the Heisenberg chain the following properties are obtained: (1) The critical behavior of the SU(2) invariant ferromagnet with spin S is studied, yielding critical exponents alpha = 1/2, nu = 1, and gamma = 2 for the specific heat, the correlation length, and the susceptibility, respectively. (2) An integrable SU(2) invariant model of the spin 1 Heisenberg chain interacting with an impurity of spin S is constructed. At low temperature for ferromagnetic coupling the impurity follows the critical behavior of the chain, i.e., alpha = 1/2 and gamma = 2. For antiferromagnetic coupling the impurity susceptibility for S = 1/2 diverges logarithmically as H to 0, while for S > 1 the impurity spin is partially compensated by the spins of the chain. (3) The linear coefficient gamma of the low temperature specific heat for the S = 1/2 Heisenberg antiferromagnetic chain is anomalous as H to 0, i.e.,limlimits _{Tto 0} limlimits _{Hto 0} gamma = 2/3 ne limlimits_{Hto 0 } limlimits_{Tto 0} gamma = [ 1+(e/pi) ^{1/2}]/3.. I obtained the following results for the onedimensional Hubbard model: (1) The thermodynamic BetheAnsatz equations for the Hubbard chain with an attractive onsite interaction U are derived. The results are discussed in special limits, e.g., U to infty, U to 0, T to infty, and T to 0. (2) The thermodynamic integral equations for the attractive Hubbard chain are solved numerically at low temperature. At low T the dominant states consist of Cooper pairs and their excitations. A critical field is obtained at T = 0, which disappears for T ne 0. the dependence of the low temperature specific heat coefficient gamma on band filling and magnetic field is obtained. The excitation spectrum is discussed in the context of superconductivity and resonant valence bonds. (3) Some unusual properties of the degenerate Hubbard chain with repulsive interaction (with more than double occupancy of the same site being excluded) are discussed. In zero field and in large degeneracy (N) limit the groundstate resembles an interacting Bose gas and 1/N contributions vanish identically. The susceptibility at T = 0 shows logarithmic singularities as H to 0 and the specific heat coefficient gamma is singular.
 Publication:

Ph.D. Thesis
 Pub Date:
 1989
 Bibcode:
 1989PhDT.......134L
 Keywords:

 Physics: Condensed Matter