Dynamics of a Quantum Spin Liquid

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Springer, Apr 5, 2016 - Technology & Engineering - 140 pages
This thesis presents an exact theoretical study of dynamical correlation functions in different phases of a two-dimensional quantum spin liquid. By calculating the dynamical spin structure factor and the Raman scattering cross section, this thesis shows that there are salient signatures—qualitative and quantitative—of the Majorana fermions and the gauge fluxes emerging as effective degrees of freedom in the exactly solvable Kitaev honeycomb lattice model. The model is a representative of a class of spin liquids with Majorana fermions coupled to Z2 gauge fields. The qualitative features of the response functions should therefore be characteristic for this broad class of topological states.
 

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Contents

1 Introduction
1
2 Kitaevs Honeycomb Lattice Model
23
Mapping to a Quantum Quench
37
4 Results for the Structure Factor
59
5 NonAbelian Phase and the Effect of Disorder
67
6 Raman Scattering
86
7 Conclusion and Outlook
99
Pfaffians from Path Integrals
105
XRay Edge and Singular Integral Equations
122
Exact Diagonalization of Four Dimers
135
Calculation of Matrix Elements
137
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About the author (2016)

Johannes Knolle completed his doctoral studies at the Max Planck Institute for the Physics of Complex Systems, Dresden, Germany (with Prof. R. Moessner). He is now a Postdoc at the Cavendish Laboratory, University of Cambridge, UK.

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