Surface energy of the one-dimensional supersymmetric $t-J$ model with general integrable boundary terms in the antiferromagnetic sector

TL;DR

This paper analyzes the surface energy of a one-dimensional supersymmetric $t-J$ model with general boundary conditions, deriving key physical quantities and identifying stable boundary bound states.

Contribution

It provides analytical expressions for the density of states, ground state energy, and surface energy, considering the effects of boundary magnetic fields in an integrable model.

Findings

Inhomogeneous term's contribution scales as $L^{eta}$ with $eta<0$

Explicit formulas for density of states and surface energy are obtained

Stable boundary bound states exist under certain boundary field conditions

Abstract

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 $L^{\beta}$ where $\beta<0$. 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.