## Dynamics of a Quantum Spin LiquidThis 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 | |

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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Abelian antiferromagnetic Baskaran behavior Bogoliubov Bogoliubov transformation bond fermion calculation component correlation function density diagonal dimer disorder Dyson equation exact solution exactly solvable experimental Fermi Fermi sea finite fluctuations flux free flux gap flux pair flux sector fractionalization frequency frustrated magnets gapless phase gauge ground state flux Hamiltonian Heisenberg model hijia honeycomb lattice isotropic point ı-function jM0i Jx D Jy Khaliullin left panel Lehmann representation Lett link variables low energy magnetic ordering Majorana fermions matrix elements matter fermions Mott insulators non-Abelian phase parity particle excitations path integrals Pfaffian phase diagram phase transition Phys physics plaquette QSL phase quantum phase quantum quench Quantum Spin Liquid Raman scattering shown single particle gap spectrum spin correlation function spin wave spinons structure factor sublattices superconductors temperature theory thermodynamic limit thesis topological order van Hove singularity X-ray edge problem zero