A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910375634534400 |
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| author | Zhang, Xin Klümper, Andreas Popkov, Vladislav |
| author_facet | Zhang, Xin Klümper, Andreas Popkov, Vladislav |
| contents | 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 to parameterize 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_00161 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain Zhang, Xin Klümper, Andreas Popkov, Vladislav Statistical Mechanics Mathematical Physics Quantum Physics 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 to parameterize 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. |
| title | A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain |
| topic | Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2312.00161 |