Exact physical quantities of the XYZ spin chain in the thermodynamic limit

TL;DR

This paper derives exact expressions for physical quantities of the XYZ spin chain in the thermodynamic limit, revealing parity-dependent effects and validating results with numerical methods.

Contribution

It introduces a novel approach using the $T-Q$ relation and Bethe root analysis to compute thermodynamic properties of the XYZ spin chain.

Findings

Surface and excitation energies depend on the parity of the number of sites.

The distribution patterns of Bethe roots and zeros are characterized.

Results are consistent with density matrix renormalization group calculations.

Abstract

The thermodynamic limits of the XYZ spin chain with periodic or twisted boundary conditions are studied. By using the technique of characterizing the eigenvalue of the transfer matrix by the $T-Q$ relation and by the zeros of the associated polynomial, we obtain the constraints of the Bethe roots and the zeros for the eigenvalues. With the help of structure of Bethe roots, we obtain the distribution patterns of zeros. Based on them, the physical quantities such as the surface energy and excitation energy are calculated. We find that both of them depend on the parity of sites number due to the topological long-range Neel order on the Mobius manifold in the spin space. We also check our results with those obtaining by the density matrix renormalization group. The method provided in this paper can be applied to study the thermodynamic properties at the thermal equilibrium state with finite temperature.