Abstract
The main objective of the thesis is to calculate the exact dynamic spin correlation function of the Kitaev QSL. As discussed in the introduction, the possibility to obtain exact results for interacting and nontrivial quantum systems is usually restricted to 1D systems, but the solubility of the Kitaev model extends this possibility to 2D. Many aspects of the Kitaev model were studied since its publication, but surprisingly no results for the full time dependence of correlation functions existed. However, a word of caution is necessary! Similar to the situation of the Bethe-Ansatz in 1D, obtaining exact spectra can be much easier than calculating exact correlation functions (Caux 2009). In fact the full spectrum of the Heisenberg chain is known since the thirties of the last century (Bethe 1931) but the full time (or frequency) dependence of the spin correlation function was just recently obtained and remains a challenging numerical task (Caux 2009; Mourigal et al. 2013). It turns out that the situation is similar in the case of the Kitaev model, for which I calculate the spin correlation function numerically exactly. I discuss at the end of this chapter what I precisely mean by numerically exact results.
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Knolle, J. (2016). Dynamic Spin Correlations: Mapping to a Quantum Quench. In: Dynamics of a Quantum Spin Liquid. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-23953-8_3
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