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arXiv:1712.04199 · Journal of High Energy Physics

Surface energy of the one-dimensional supersymmetric t − J model with unparallel boundary fields

Fakai Wen, Zhan-Ying Yang, Tao Yang, Kun Hao, Junpeng Cao, Wen‐Li Yang

Published Jun 1, 2018• 8 citations
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Abstract

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.

DOI
10.1007/jhep06(2018)076

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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.
We investigate the thermodynamic limit of the su(n)-invariant spin chain models with unparallel boundary fields. It is found that the contribution of the inhomogeneous term in the associated T–Q relation to the ground state energy does vanish in the thermodynamic limit. This fact allows us to calculate the boundary energy of the system. Taking the su(2) (or the XXX) spin chain and the su(3) spin chain as concrete examples, we have studied the corresponding boundary energies of the models. The method used in this paper can be generalized to study the thermodynamic properties and boundary energy of other high rank models with non-diagonal boundary fields.
The thermodynamic limit and boundary energy of the isotropic spin-1 Heisenberg chain with non-diagonal boundary fields are studied. The finite size scaling properties of the inhomogeneous term in the T-Q relation at the ground state are calculated by the density matrix renormalization group. Based on our findings, the boundary energy of the system in the thermodynamic limit can be obtained from Bethe ansatz equations of a related model with parallel boundary fields. These results can be generalized to the SU(2) symmetric high spin Heisenberg model directly.
Abstract The thermodynamic properties of the XXZ spin chain with integrable open boundary conditions at the gaped region (i.e. the anisotropic parameter being a real number) are investigated. It is shown that the contribution of the inhomogeneous term in the T − Q relation of the ground state and elementary excited state can be neglected when the size of the system N tends to infinity. The surface energy and elementary excitations induced by the unparallel boundary magnetic fields are obtained.