SciPost Thesis Link
| Title: | Dynamics of Heisenberg spin chains | |
| Author: | R.L. Hagemans | |
| As Contributor: | (not claimed) | |
| Type: | Ph.D. | |
| Field: | Physics | |
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| Approach: | Theoretical | |
| URL: | http://hdl.handle.net/11245/1.271001 | |
| Degree granting institution: | University of Amsterdam | |
| Supervisor(s): | J.-S. Caux | |
| Defense date: | 2007-04-12 |
Abstract:
Outline of this thesis In the next chapter, based on Bethe’s famous article, I will give an introduction to the coordinate Bethe ansatz for the XXZ and XXX chains, and derive the Bethe equations. This will also serve to introduce conventions and notations to be used throughout the thesis. Chapter 3 then addresses many subtleties of finding solutions to the Bethe equations, in particular the structure of complex solutions. In this chapter, I outline a numerical method that succeeds in finding the largest class of those solutions, in finite chains, to machine precision. In chapter 4, I discuss a method of calculating the dynamical structure factor from the solutions of Bethe’s equations on a finite chain, which is then applied to several experimentally relevant cases. Chapter 5 changes the focus to the infinite chain; here, I give results for the dynamical structure factor in the thermodynamic limit. Chapter 6 is devoted to the connection between the results of the previous chapters and the field theory approach to the same problems. Finally, I draw general conclusions and discuss possible directions for future research.