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Register a new userSurface energy of the one-dimensional supersymmetric $t-J$ model with unparallel boundary fields
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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.
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We investigate the thermodynamic limit of the inhomogeneous T-Q relation of the antiferromagnetic XXZ spin chain with antiperiodic boundary condition. It is shown that the contribution of the inhomogeneous term at the ground state can be neglected when the system-size N tends to infinity, which enables us to reduce the inhomogeneous Bethe ansatz equations (BAEs) to the homogeneous ones. Then the quantum numbers at the ground states are obtained, by which the system with arbitrary size can be studied. We also calculate the twisted boundary energy of the system.
The quantum $tau_2$-model with generic site-dependent inhomogeneity and arbitrary boundary fields is studied via the off-diagonal Bethe Ansatz method. The eigenvalues of the corresponding transfer matrix are given in terms of an inhomogeneous T-Q relation, which is based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices. Moreover, the associated Bethe Ansatz equations are also obtained.
In this first paper, we start the analysis of correlation functions of quantum spin chains with general integrable boundary conditions. We initiate these computations for the open XXX spin 1/2 quantum chains with some unparallel magnetic fields allowing for a spectrum characterization in terms of homogeneous Baxter like TQ-equations, in the framework of the quantum separation of variables (SoV). Previous SoV analysis leads to the formula for the scalar products of the so-called separate states. Here, we solve the remaining fundamental steps allowing for the computation of correlation functions. In particular, we rederive the ground state density in the thermodynamic limit thanks to SoV approach, we compute the so-called boundary-bulk decomposition of boundary separate states and the action of local operators on these separate states in the case of unparallel boundary magnetic fields. These findings allow us to derive multiple integral formulae for these correlation functions similar to those previously known for the open XXX quantum spin chain with parallel magnetic fields.
Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge transformations, proper generators and reference state for constructing Bethe vectors can be obtained respectively. Given an inhomogeneous T-Q relation for an eigenvalue, it is proven that the resulting Bethe state is an eigenstate of the transfer matrix, provided that the parameters of the generators satisfy the associated Bethe Ansatz equations.
The $t$-$J$ model is a standard model of strongly correlated electrons, often studied in the context of high-$T_c$ superconductivity. However, most studies of this model neglect three-site terms, which appear at the same order as the superexchange $J$. As these terms correspond to pair-hopping, they are expected to play an important role in the physics of superconductivity when doped sufficiently far from half-filling. In this paper we present a density matrix renormalisation group study of the one-dimensional $t$-$J$ model with the pair hopping terms included. We demonstrate that that these additional terms radically change the one-dimensional ground state phase diagram, extending the superconducting region at low fillings, while at larger fillings, superconductivity is completely suppressed. We explain this effect by introducing a simplified effective model of repulsive hardcore bosons.
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