Exact ground state and elementary excitations of a topological spin chain

Abstract

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.

arXiv commentPublished version, 6 pages, 3 figures

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• Exact physical quantities of the $D_2^{(2)}$ spin chain model with generic open boundary conditions
• Exact physical quantities of a competing spin chain in the thermodynamic limit
• 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