Gonzalez Hurtado, Rebeca (2026) How the Coordinate Bethe Ansatz works for the Haldane-Shastry Spin Chain Model. Bachelor's Thesis, Physics.
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Abstract
This report is a study of the ferromagnetic Haldane-Shastry spin chain when analyzed via the Coordinate Bethe Ansatz. The aim was to describe the energy spectrum of the spin chain by solving the eigenvalue problem between the Hamiltonian and the eigenvalues to arrive at conclusions about the structure and implications of the CBA on the long-range interaction spin chain. The Haldane-Shastry spin chain describes a 1D quantum spin-$\frac{1}{2}$ model with long-range interactions, and the CBA is a wavefunction proposed to solve the system. The CBA was used to solve the Heisenberg model by Bethe, and literature already suggests that the freezing trick produces the structure of the wavefunction that successfully incorporates the inverse interaction behavior with two Slater determinants. Instead, this paper studies the applications on the Haldane-Shastry model via the CBA, suggesting that the structure of the CBA exhibits some appropriate but incomplete interaction behavior. First, the ground and first excited states were found by exploiting symmetries and the imposed periodic boundary conditions. Then, the CBA was applied for the 2-magnon case, where the interaction terms were scaled with a scattering ratio of $\frac{A'}{A} = -1$ to produce a single Slater determinant. A state for the 2-magnon case that includes a cross interaction term was proposed as an egienstate that more accurately describes the inverse square interaction behavior to produce a determinant squared.
| Item Type: | Thesis (Bachelor's Thesis) |
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| Supervisor name: | Gorbe, T.F. and Hoekstra, S. |
| Degree programme: | Physics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 27 Mar 2026 10:24 |
| Last Modified: | 27 Mar 2026 10:24 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37269 |
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