arXiv:2112.07180 · Nuclear Physics B

Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η = i π 3

Pei Sun, Jintao Yang, Yi Qiao, Junpeng Cao, Wen‐Li Yang

Published Dec 8, 2021• 1 citation

Abstract

We study the thermodynamic limit of the antiperiodic XXZ spin chain with the anisotropic parameter η=πi3. We parameterize eigenvalues of the transfer matrix by their zero points instead of Bethe roots. We obtain patterns of the distribution of zero points. Based on them, we calculate the ground state energy and the elementary excitations in the thermodynamic limit. We also obtain the two-body scattering matrix of elementary excitations. Two types of elementary excitations and three types of scattering processes are discussed in detailed.

DOI: 10.1016/j.nuclphysb.2021.115626

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arXiv:2112.07180 · Nuclear Physics B

Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η = i π 3

Pei Sun, Jintao Yang, Yi Qiao, Junpeng Cao, Wen‐Li Yang

Published Dec 8, 2021• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.1016/j.nuclphysb.2021.115626

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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.

The exact elementary excitations in a typical

U(1)

symmetry broken quantum integrable system, that is the twisted ${J}_{1}\ensuremath{-}{J}_{2}$ spin chain with nearest-neighbor, next nearest neighbor, and chiral three spin interactions, are studied. The main technique is that we quantify the energy spectrum of the system by the zero roots of the transfer matrix instead of the traditional Bethe roots. From the numerical calculation and singularity analysis, we obtain the patterns of zero roots. Based on them, we analytically obtain the ground state energy and the elementary excitations in the thermodynamic limit. We find that the system also exhibits the nearly degenerate states in the regime of $\ensuremath{\eta}\ensuremath{\in}\mathbb{R}$, where the nearest-neighbor couplings among the

z

direction are ferromagnetic. More careful study shows that the competing of interactions can induce the gapless low-lying excitations and quantum phase transition in the antiferromagnetic regime with $\ensuremath{\eta}\ensuremath{\in}\mathbb{R}+i\ensuremath{\pi}$.