This thesis is a tour-de-force combination of analytic and computational results clarifying and resolving important questions about the nature of quantum phase transitions in one- and two-dimensional magnetic systems. The author presents a comprehensive study of a low-dimensional spin-half quantum antiferromagnet (the J-Q model) in the presence of a magnetic field in both one and two dimensions, demonstrating the causes of metamagnetism in such systems and providing direct evidence of fractionalized excitations near the deconfined quantum critical point. In addition to describing significant new research results, this thesis also provides the non-expert with a clear understanding of the nature and importance of computational physics and its role in condensed matter physics as well as the nature of phase transitions, both classical and quantum. It also contains an elegant and detailed but accessible summary of the methods used in the thesis-exact diagonalization, Monte Carlo, quantum Monte Carlo and the stochastic series expansion-that will serve as a valuable pedagogical introduction to students beginning in this field.

Autorentext
Adam Iaizzi received his PhD from Boston University in 2018. He now holds a postdoctoral position at National Taiwan University.

Inhalt
1 Introduction 11.1 How to Read this Dissertation . . . . . . . . . . . . . . . . . . . . . . 21.2 What is Computational Physics? . . . . . . . . . . . . . . . . . . . . 31.2.1 A Brief History of Computational Physics . . . . . . . . . . . 51.2.2 Development of the Metropolis Algorithm . . . . . . . . . . . 71.2.3 Toward a More Detailed Balance . . . . . . . . . . . . . . . . 91.3 Condensed Matter Physics . . . . . . . . . . . . . . . . . . . . . . . . 151.4 Classical Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . . 171.4.1 2D Ising Model . . . . . . . . . . . . . . . . . . . . . . . . . . 201.5 Quantum Phase Transitions . . . . . . . . . . . . . . . . . . . . . . . 261.5.1 Deconned Quantum Criticality . . . . . . . . . . . . . . . . . 311.5.2 What are Quasiparticles? . . . . . . . . . . . . . . . . . . . . . 321.6 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352 Saturation Transition in the 1D J-Q Model 382.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412.3 Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.4 Metamagnetism in the J-Q Chain . . . . . . . . . . . . . . . . . . . 462.4.1 Origin of the Magnetization Jump . . . . . . . . . . . . . . . . 492.4.2 An Exact Solution at qmin . . . . . . . . . . . . . . . . . . . . 542.4.3 Excluded Mechanisms for Metamagnetism . . . . . . . . . . . 552.5 Metamagnetism in the J1-J2 Chain . . . . . . . . . . . . . . . . . . . 572.6 Zero-Scale-Factor Universality . . . . . . . . . . . . . . . . . . . . . . 612.7 Conclusions and Discussion . . . . . . . . . . . . . . . . . . . . . . . 683 Saturation Transition in the 2D J-Q Model 713.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.3 Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.4 Metamagnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763.4.1 Exact Solution for qmin . . . . . . . . . . . . . . . . . . . . . 773.4.2 Quantum Monte Carlo Results . . . . . . . . . . . . . . . . . . 803.5 Zero-Scale-Factor Universality in 2D . . . . . . . . . . . . . . . . . . 823.5.1 Form of the Low-Temperature Divergence . . . . . . . . . . . 853.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914 Signatures of Deconned Quantum Criticality in the 2D J-Q-h Model 934.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.1.1 The Zero-eld J-Q Model . . . . . . . . . . . . . . . . . . . . 944.1.2 Anomalous Specic Heat . . . . . . . . . . . . . . . . . . . . . 964.1.3 BKT Transition . . . . . . . . . . . . . . . . . . . . . . . . . 974.1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.3 Phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.4 Field-induced BKT Transition . . . . . . . . . . . . . . . . . . . . . 1024.4.1 Spin Stiness . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.4.2 Non-monotonic m(T) Dependence . . . . . . . . . . . . . . . . 1074.4.3 Estimation of TBKT . . . . . . . . . . . . . . . . . . . . . . . . 1114.5 Anomalous Specic Heat . . . . . . . . . . . . . . . . . . . . . . . . 1124.5.1 Contributions from the Gapless Modes . . . . . . . . . . . . . 1154.5.2 QMC Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 1204.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255 Methods 1275.1 Exact Diagonalization . . . . . . . . . . . . . . . . . . . . . . . . . . 1285.2 Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . ...