Entanglement in Quantum Lifshitz Theories

In recent years, the study of entanglement properties of quantum field theories has led to deep insights in fields as diverse as quantum gravity and condensed matter physics. Originating as effective field theories for certain quantum dimer models, the Quantum Lifshitz Model (QLM) and its generalizations are bosonic quantum field theories with anisotropic scaling symmetry between space and time. Being closely related to conformal field theories, they provide a fruitful playground, where diverse entanglement calculations can be performed analytically. In this thesis, we concentrate on two entanglement measures, the entanglement entropy and logarithmic negativity. Motivated to extract sub-leading universal behavior, we perform analytic calculations in two and higher even dimensions. In order to make the calculations tractable, we put the QLM on compact manifolds, such as spheres and tori, where the spectrum of a certain operator appearing in the ground state of the theory is explicitly known. Mostly by means of the replica method, we then find analytic expressions for the finite sub-leading terms of the entanglement entropy and logarithmic negativity of the ground state, as well as the entanglement entropy of the excited states of the QLM. In the case of the ground state entanglement entropy, we provide analytic expressions for the sub-leading terms as functions of the dimension and the dynamical critical exponent. For the excited states we provide analytic formulae of the sub-leading coefficients as functions of the excitation numbers.