Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields

Abstract

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 $N\to \infty$. 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 spinon-like excitations, which obviously do not carry spin-$\frac{1}{2}$, are observed. The present method provides an universal procedure to deal with quantum integrable systems either with or without $U(1)$ symmetry.

arXiv comment6 pages, 4 figures

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• T-W relation and free energy of the Heisenberg chain at a finite temperature
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• Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit
• Off-diagonal approach to the exact solution of quantum integrable systems
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• Scattering matrix of elementary excitations in the antiperiodic XXZ spin chain with η=iπ/3
• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Exact surface energies and boundary excitations of the Izergin-Korepin model with generic boundary fields
• Exact physical quantities of a competing spin chain in the thermodynamic limit
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• T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature
• Exact physical quantities of the XYZ spin chain in the thermodynamic limit