Dynamics and entanglement of exotic quantum liquids

Thesis

This thesis focuses on the one-dimensional Hubbard model, considering both dynamical response functions and also particular entanglement measures of highly excited eigenstates.

In Chapter 2 we discuss how to describe the optical conductivity at finite energy scales. In order to calculate the dynamical response of this interacting system, it is necessary to go beyond the conventional Luttinger liquid picture. Using mobile impurity models and integrability we make quantitative predictions which can be compared with numerics.

In Chapter 3, we investigate the existence of the so-called "quantum disentangled liquid" (QDL) in the same system. The diagnostic for the QDL involves understanding the bipartite entanglement entropy of highly excited eigenstates. Here we use results from integrability and strong-coupling expansions to argue that such a state of matter is realised in the Hubbard chain in a specific sense.

Authors: Veness, T

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford