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International Journal of Modern Physics B

Finite-Size Corrections in the Supersymmetric t–J Model with Boundary Fields

Hitoshi Asakawa, Masuo Suzuki

Published Apr 10, 1997• 11 citations
Publisher

Abstract

The supersymmetric t–J model with boundary fields is discussed. Using the exact solution of the present model, the finite-size corrections of the ground-state energy and the low-lying excitation energies are calculated. The partition functions are evaluated in the scaling limit to obtain the conformal weights of the primary fields in the present model. A surface critical exponent and the ground-state degeneracy are also derived.

DOI
10.1142/s0217979297000575

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The supersymmetric t–J model with boundary fields is discussed. Using the exact solution of the present model, the finite-size corrections of the ground-state energy and the low-lying excitation energies are calculated. The partition functions are evaluated in the scaling limit to obtain the conformal weights of the primary fields in the present model. A surface critical exponent and the ground-state degeneracy are also derived.
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Abstract We investigate the thermodynamic limit of the exact solution, which is given by an inhomogeneous T − Q relation, of the one-dimensional supersymmetric t − J model with unparallel boundary magnetic fields. It is shown that the contribution of the inhomogeneous term at the ground state satisfies the L −1 scaling law, where L is the system-size. This fact enables us to calculate the surface (or boundary) energy of the system. The method used in this paper can be generalized to study the thermodynamic limit and surface energy of other models related to rational R-matrices.
In this paper, we study the surface energy of the one-dimensional supersymmetric t-J model with unparallel boundary magnetic fields, which is a typical U(1)-symmetry broken quantum integrable strongly correlated electron system. It is shown that at the ground state, the contribution of inhomogeneous term in the Bethe ansatz solution of eigenvalues of transfer matrix satisfies the finite size scaling law L^β where β<0. Based on it, the physical quantities of the system in the thermodynamic limit are calculated. We obtain the patterns of Bethe roots and the analytical expressions of density of states, ground state energy and surface energy. We also find that there exist the stable boundary bound states if the boundary fields satisfy some constraints.
Quantum integrability is established for the one-dimensional supersymmetric UUU model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric UUU chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system.