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Register a new userSurface energy and elementary excitations of the XXZ spin chain with arbitrary boundary fields
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The thermodynamic properties of the XXZ spin chain with integrable open boundary conditions at the gaped region (i.e., the anisotropic parameter $eta$ 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.
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An analytic method is proposed to compute the surface energy and elementary excitations of the XXZ spin chain with generic non-diagonal boundary fields. For the gapped case, in some boundary parameter regimes the contributions of the two boundary fields to the surface energy are non-additive. Such a correlation effect between the two boundaries also depends on the parity of the site number $N$ even in the thermodynamic limit $Ntoinfty$. For the gapless case, contributions of the two boundary fields to the surface energy are additive due to the absence of long-range correlation in the bulk. Although the $U(1)$ symmetry of the system is broken, exact spinon-like excitations, which obviously do not carry spin-$frac12$, are observed. The present method provides an universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry.
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.
A novel Bethe Ansatz scheme is proposed to calculate physical properties of quantum integrable systems without $U(1)$ symmetry. As an example, the anti-periodic XXZ spin chain, a typical correlated many-body system embedded in a topological manifold, is examined. Conserved momentum and charge operators are constructed despite the absence of translational invariance and $U(1)$ symmetry. The ground state energy and elementary excitations are derived exactly. It is found that two intrinsic fractional (one half) zero modes accounting for the double degeneracy exist in the eigenstates. The elementary excitations show quite a different picture from that of a periodic chain. This method can be applied to other quantum integrable models either with or without $U(1)$ symmetry.
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 have investigated the zero and finite temperature behaviors of the anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of a transverse magnetic field (h). The attention is concentrated on an interval of magnetic field between the factorizing field (h_f) and the critical one (h_c). The model presents a spin-flop phase for 0<h<h_f with an energy scale which is defined by the long range antiferromagnetic order while it undergoes an entanglement phase transition at h=h_f. The entanglement estimators clearly show that the entanglement is lost exactly at h=h_f which justifies different quantum correlations on both sides of the factorizing field. As a consequence of zero entanglement (at h=h_f) the ground state is known exactly as a product of single particle states which is the starting point for initiating a spin wave theory. The linear spin wave theory is implemented to obtain the specific heat and thermal entanglement of the model in the interested region. A double peak structure is found in the specific heat around h=h_f which manifests the existence of two energy scales in the system as a result of two competing orders before the critical point. These results are confirmed by the low temperature Lanczos data which we have computed.
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