An Exploration of Quantum Critical Phenomena in One-Dimensional Lattice Systems: Geometric Frustration & Quantum Fluctuations

  • Christine Cartwright

Student thesis: Doctoral ThesisDoctor of Philosophy

Abstract

This thesis focuses on identifying different types of critical phenomena within one-dimensional quantum lattice spin systems. People are exposed to classical critical phenomena everyday in the form of phase transitions, such as from water to ice. Surrounding quantum phase transitions, there is a number of exciting phenomena still to be explored, enhancing our knowledge of the quantum effects.

We will examine the features of quantum phase transitions within spin chains, where our focus will be on the use of entanglement measures, and we will explore an extension of the standard Bose-Hubbard model on a one-dimensional lattice with a non-trivial elementary cell.

Our first main focus will be on the use of entanglement scaling as an indicator of when a phase transition has occurred, more specifically for first-order quantum phase transitions in the vicinity of second-order quantum phase transitions. In this context, we show the dramatic importance of finite-size effects when a first-order quantum phase transition occurs in the nearby region of multi-critical point containing also a second-order quantum phase transition. Through the use of finite-size scaling we highlight that a bipartite measure of entanglement can correctly identify a given first-order quantum phase transition.

Motivated by the plethora of diverse features that geometric frustration may lead to, we will also examine the Bose-Hubbard model on a geometrically frustrated lattice. The lattice we will examine is a one-dimensional chain of rhombi and causes the particles to form pairs in the presence of repulsive interactions. We perform a detailed numerical analysis of the different phases emerging from the model, including the block entropy and entanglement spectrum. Additionally, we perform an analysis of the model under dynamics with a single, a pair of particles and for unit filling.
Date of Award2019
Original languageEnglish
Awarding Institution
  • Queen's University Belfast
SupervisorGabriele De Chiara (Supervisor)

Cite this

An Exploration of Quantum Critical Phenomena in One-Dimensional Lattice Systems: Geometric Frustration & Quantum Fluctuations
Cartwright, C. (Author). 2019

Student thesis: Doctoral ThesisDoctor of Philosophy