Non-equivalence between Heisenberg XXZ spin chain and Thirring model
T. Fujita, T. Kobayashi, M. Hiramoto, H. Takahashi
TL;DR
This paper investigates the relationship between the Heisenberg XXZ spin chain and the Thirring model, demonstrating that their spectra are not equivalent, contrary to some previous assumptions, through numerical solutions of Bethe ansatz equations.
Contribution
It provides a numerical analysis showing the non-equivalence of the XXZ spin chain spectrum and the regularized Thirring model spectrum.
Findings
The Bethe ansatz equations are numerically solved for the XXZ spin chain.
The spectrum of the XXZ spin chain differs from that of the Thirring model.
The results challenge the assumption of spectral equivalence between the models.
Abstract
The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are numerically solved, and the energy eigenvalues are determined for the anti-ferromagnetic case. We examine the relation between the XXZ spin chain and the Thirring model, and show that the spectrum of the XXZ spin chain is different from that of the regularized Thirring model.
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