Root patterns and energy spectra of quantum integrable systems without U(1) symmetry: the antiperiodic XXZ spin chain

Finding out root patterns of quantum integrable models is an important step to study their physical properties in the thermodynamic limit. Especially for models without U(1) symmetry, their spectra are usually given by inhomogeneous T - Q relations and the Bethe root patterns are still unclear. In this paper with the antiperiodic XXZ spin chain as an example, an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit is proposed. Based on them the ground state energy and elementary excitations in the gapped regime are derived. The present method provides an universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.

Automated summary

The paper proposes an analytic method to derive both the Bethe root patterns and the transfer-matrix root patterns in the thermodynamic limit, using the antiperiodic XXZ spin chain as an example. Based on these patterns, the ground state energy and elementary excitations in the gapped regime are derived. This method provides a universal procedure to compute physical properties of quantum integrable models in the thermodynamic limit.