Diagnosing criticality in symmetric and chiral clock models

Pecorari, Laura (2022) Diagnosing criticality in symmetric and chiral clock models. [Laurea magistrale], Università di Bologna, Corso di Studio in Physics [LM-DM270]
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Abstract

Quantum clock models are statistical mechanical spin models which may be regarded as a sort of bridge between the one-dimensional quantum Ising model and the one-dimensional quantum XY model. This thesis aims to provide an exhaustive review of these models using both analytical and numerical techniques. We present some important duality transformations which allow us to recast clock models into different forms, involving for example parafermions and lattice gauge theories. Thus, the notion of topological order enters into the game opening new scenarios for possible applications, like topological quantum computing. The second part of this thesis is devoted to the numerical analysis of clock models. We explore their phase diagram under different setups, with and without chirality, starting with a transverse field and then adding a longitudinal field as well. The most important observables we take into account for diagnosing criticality are the energy gap, the magnetisation, the entanglement entropy and the correlation functions.

Abstract
Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Pecorari, Laura
Relatore della tesi
Correlatore della tesi
Scuola
Corso di studio
Indirizzo
THEORETICAL PHYSICS
Ordinamento Cds
DM270
Parole chiave
phase transitions,statistical mechanics,clock models,Potts model,chiral clock models,duality transformations,DMRG
Data di discussione della Tesi
16 Dicembre 2022
URI

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