Foundations and Applications of Entanglement Renormalization

TL;DR

This paper discusses entanglement renormalization, a novel numerical method combining renormalization group ideas and quantum information to better understand complex quantum many-body systems and phenomena.

Contribution

It provides a comprehensive overview of entanglement renormalization's development, algorithms, and applications in quantum criticality and frustrated spin systems.

Findings

ER can simulate quantum critical phenomena effectively

Development of optimization algorithms for ER

Initial applications to simple free particle systems

Abstract

Understanding the collective behavior of a quantum many-body system, a system composed of a large number of interacting microscopic degrees of freedom, is a key aspect in many areas of contemporary physics. However, as a direct consequence of the difficultly of the so-called many-body problem, many exotic quantum phenomena involving extended systems, such as high temperature superconductivity, remain not well understood on a theoretical level. Entanglement renormalization is a recently proposed numerical method for the simulation of many-body systems which draws together ideas from the renormalization group and from the field of quantum information. By taking due care of the quantum entanglement of a system, entanglement renormalization has the potential to go beyond the limitations of previous numerical methods and to provide new insight to quantum collective phenomena. This thesis comprises a significant portion of the research development of ER following its initial proposal. This includes exploratory studies with ER in simple systems of free particles, the development of the optimisation algorithms associated to ER, and the early applications of ER in the study of quantum critical phenomena and frustrated spin systems.