arXiv:2404.19240 · Journal of High Energy Physics

Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields

Zhirong Xin, Junpeng Cao, Wen‐Li Yang, Yupeng Wang

Published Oct 10, 2024• 2 citations

Abstract

A bstract We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N , due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.

DOI: 10.1007/jhep10(2024)090

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arXiv:2404.19240 · Journal of High Energy Physics

Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields

Zhirong Xin, Junpeng Cao, Wen‐Li Yang, Yupeng Wang

Published Oct 10, 2024• 2 citations

arXiv HTML PDF

Abstract

DOI: 10.1007/jhep10(2024)090

Related papers

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N

even in the thermodynamic limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$. 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 spinonlike excitations, which obviously do not carry spin-

\frac{1}{2}

, are observed. The present method provides a universal procedure to deal with quantum integrable systems either with or without

U(1)

symmetry.

Thermodynamic limit of the spin-

\frac{1}{2}

XYZ spin chain with the antiperiodic boundary condition

Abstract Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-

\frac{1}{2}

1 2 XYZ spin chain with the antiperiodic boundary condition. The key point of our method is that there exist some degenerate points of the crossing parameter ηm,l, at which the associated inhomogeneous T − Q relation becomes a homogeneous one. This makes extrapolating the formulae deriving from the homogeneous one to an arbitrary η with O(N−2) corrections for a large N possible. The ground state energy and elementary excitations of the system are obtained. By taking the trigonometric limit, we also give the results of antiperiodic XXZ spin chain within the gapless region in the thermodynamic limit, which does not have any degenerate points.

Exact physical quantities of the

{D}_2^{(2)}

spin chain model with generic open boundary conditions

A bstract We study the quantum integrable spin chain model associated with the twisted

{D}_2^{(2)}

D 2 2 algebra (or simply the

{D}_2^{(2)}

D 2 2 model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two staggered XXZ spin chains. Applying the t - W method, we derive the homogeneous Bethe ansatz equations for the zeros of the transfer matrix eigenvalues and the patterns of the corresponding zeros of the staggered XXZ spin chain with generic integrable boundaries. Based on these results, we analytically compute the surface energies and excitation energies of the

{D}_2^{(2)}

D 2 2 model in different regimes of boundary parameters.