Work

Pedestrian's way to Baxter's Bethe ansatz for the periodic XYZ chain

Year: 2024

Type: article

Abstract: A chiral coordinate Bethe ansatz method is developed to study the periodic XYZ chain. We construct a set of chiral vectors with fixed number of kinks. All vectors are factorized and have simple structures. Under roots of unity conditions, the Hilbert space has an invariant subspace, and our vectors form a basis of this subspace. We propose a Bethe ansatz solely based on the action of the Hamiltonian on the chiral vectors, avoiding the use of transfer matrix techniques. This allows us to parametrize the expansion coefficients and derive the homogeneous Bethe ansatz equations, whose solutions give the exact energies and eigenstates. Our analytic results agree with earlier approaches, notably by Baxter, and are supported by numerical calculations.

Source: Physical review. B./Physical review. B

DOI: 10.1103/physrevb.109.115411

Authors: Xin Zhang, Andreas Klümper, Vladislav Popkov

Institutions: Chinese Academy of Sciences, Institute of Physics, University of Wuppertal, University of Ljubljana

Language: English

Topic: Quantum many-body systems

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Deutsche Forschungsgemeinschaft, National Natural Science Foundation of China

Awards: G1170140333, G136828775, G6923507189