Thermodynamic limit of the spin-$\frac{1}{2}$ XYZ spin chain with the antiperiodic boundary condition

TL;DR

This paper analyzes the thermodynamic limit of the spin-1/2 XYZ chain with antiperiodic boundary conditions using off-diagonal Bethe ansatz, revealing ground state energy and excitations, and extends results to the XXZ limit.

Contribution

It introduces a method leveraging degenerate crossing points to simplify the analysis of the XYZ chain's thermodynamic limit, including the homogeneous $T-Q$ relation extrapolation.

Findings

Ground state energy and elementary excitations obtained.

Method applicable to large N with O(N^{-2}) corrections.

Results extended to the antiperiodic XXZ chain in the gapless region.

Abstract

Based on its off-diagonal Bethe ansatz solution, we study the thermodynamic limit of the spin-$\frac{1}{2}$ 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 $\eta_{m,l}$, 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 $\eta$ 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.