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Register a new userCorrelation functions of the XXZ spin chain with the twisted boundary condition
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The scalar products, form factors and correlation functions of the XXZ spin chain with twisted (or antiperiodic) boundary condition are obtained based on the inhomogeneous $T-Q$ relation and the Bethe states constructed via the off-diagonal Bethe Ansatz. It is shown that the scalar product of two off-shell Bethe states, the form factors and the two-point correlation functions can be expressed as the summation of certain determinants. The corresponding homogeneous limits are studied. The results are also checked by the numerical calculations.
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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.
We investigate the thermodynamic limit of the one-dimensional ferromagnetic XXZ model with twisted (or antiperiodic ) boundary condition. It is shown that the distribution of the Bethe roots of the inhomogeneous Bethe Ansatz equations (BAEs) for the ground state as well as for the low-lying excited states satisfy the string hypothesis, although the inhomogeneous BAEs are not in the standard product form which has made the study of the corresponding thermodynamic limit nontrivial. We also obtain the twisted boundary energy induced by the non-trivial twisted boundary conditions in the thermodynamic limit.
The exact solution of an integrable anisotropic Heisenberg spin chain with nearest-neighbour, next-nearest-neighbour and scalar chirality couplings is studied, where the boundary condition is the antiperiodic one. The detailed construction of Hamiltonian and the proof of integrability are given. The antiperiodic boundary condition breaks the $U(1)$-symmetry of the system and we use the off-diagonal Bethe Ansatz to solve it. The energy spectrum is characterized by the inhomogeneous $T-Q$ relations and the contribution of the inhomogeneous term is studied. The ground state energy and the twisted boundary energy in different regions are obtained. We also find that the Bethe roots at the ground state form the string structure if the coupling constant $J=-1$ although the Bethe Ansatz equations are the inhomogeneous ones.
We consider the Heisenberg XXZ spin-$J$ chain ($Jinmathbb{N}/2$) with anisotropy parameter $Delta$. Assuming that $Delta>2J$, and introducing threshold energies $E_{K}:=Kleft(1-frac{2J}{Delta}right)$, we show that the bipartite entanglement entropy (EE) of states belonging to any spectral subspace with energy less than $E_{K+1}$ satisfy a logarithmically corrected area law with prefactor $(2lfloor K/Jrfloor-2)$. This generalizes previous results by Beaud and Warzel as well as Abdul-Rahman, Stolz and one of the authors, who covered the spin-$1/2$ case.
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.
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