The Bologna Lectures
13-26 November 2016
This short graduate course introduces modern quantum field theory approaches to the computation of measures of entanglement and to the description of many-body quantum systems out of equilibrium. The focus is on quantum field theory in one time and one space dimension and mostly on integrable quantum field theory.
We start by reviewing some classical ideas in the study of 1+1-dimensional quantum integrable models: integrable models as massive perturbations of conformal field theories and conformal field theories as effective descriptions of quantum critical points.
We review two widely used approaches to the study of quantum integrable models in 1+1 dimensions: the thermodynamic Bethe ansatz and the form factor approach.
In the remainder of the course, we show how these two approaches have recently found new applications to areas of current intense interest. First, the form factor approach can be generalised in such as way as to provide a new way to study measures of entanglement in gapped systems. Second, the thermodynamic Bethe ansatz can be generalised to provide a description of important features of quantum systems out-of-equilibrium. For this part of the course, we will mainly describe our own results.
We start by reviewing some classical ideas in the study of 1+1-dimensional quantum integrable models: integrable models as massive perturbations of conformal field theories and conformal field theories as effective descriptions of quantum critical points.
We review two widely used approaches to the study of quantum integrable models in 1+1 dimensions: the thermodynamic Bethe ansatz and the form factor approach.
In the remainder of the course, we show how these two approaches have recently found new applications to areas of current intense interest. First, the form factor approach can be generalised in such as way as to provide a new way to study measures of entanglement in gapped systems. Second, the thermodynamic Bethe ansatz can be generalised to provide a description of important features of quantum systems out-of-equilibrium. For this part of the course, we will mainly describe our own results.