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

Abstract

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.

arXiv comment19 pages, 8 figures

References in corpus (10)

• The density-matrix renormalization group
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• Diffusion and ballistic transport in one-dimensional quantum systems
• Off-diagonal Bethe ansatz and exact solution of a topological spin ring
• Integrable open spin chains from giant gravitons
• Exact solution for the spin-$s$ XXZ quantum chain with non-diagonal twists
• Inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin
• Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
• Exact ground state and elementary excitations of a topological spin chain
• Thermodynamic limit and twisted boundary energy of the XXZ spin chain with antiperiodic boundary condition

Cited by in corpus (1)

• Elementary excitations in an integrable twisted J1-J2 spin chain in the thermodynamic limit