Magnetic field effects in low-dimensional quantum magnets. ([2018])

• Record Type: Book
• Further Information: Note: Adam Iaizzi.
• Authors: Iaizzi, Adam
• Contents: 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1295.2.1 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . 1325.2.2 What is a Markov Process? . . . . . . . . . . . . . . . . . . . 1335.2.3 The Metropolis-Hastings Algorithm . . . . . . . . . . . . . . . 1355.2.4 Practical Considerations: Autocorrelations, Binning, Error Bars, and Equilibration . . . . . . . . . . . . . . . . . . . . . . . . 1375.3 Quantum Monte Carlo: The Stochastic Series Expansion . . . . . . . 1405.3.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1415.3.2 Sampling Procedure . . . . . . . . . . . . . . . . . . . . . . . 1465.4 The Heisenberg Model . . . . . . . . . . . . . . . . . . . . . . . . . . 1485.4.1 Diagonal Updates . . . . . . . . . . . . . . . . . . . . . . . . . 1525.4.2 O-diagonal Updates . . . . . . . . . . . . . . . . . . . . . . . 1555.4.3 Observables in SSE . . . . . . . . . . . . . . . . . . . . . . . 1605.5 The J-Q2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1635.5.1 Diagonal Updates . . . . . . . . . . . . . . . . . . . . . . . . . 1655.5.2 O-diagonal Updates . . . . . . . . . . . . . . . . . . . . . . . 1675.6 The Heisenberg Model in an External Field . . . . . . . . . . . . . . 1685.6.1 Diagonal Updates . . . . . . . . . . . . . . . . . . . . . . . . . 1715.6.2 O-diagonal updates . . . . . . . . . . . . . . . . . . . . . . . 1735.7 The J-Q-h Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1825.7.1 Diagonal Updates . . . . . . . . . . . . . . . . . . . . . . . . . 1835.7.2 Directed Loop Updates . . . . . . . . . . . . . . . . . . . . . . 1855.8 Supplementary Procedures . . . . . . . . . . . . . . . . . . . . . . . 1855.8.1 Quantum Replica Exchange . . . . . . . . . . . . . . . . . . . 1875.8.2 Doubling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1895.9 Pseudorandom Number Generation . . . . . . . . . . . . . . . . . . . 1916 Conclusions 192A Supplementary Material for the 1D Few-magnon Expansion 194A.1 Few Magnons in the J-Q-h Chain . . . . . . . . . . . . . . . . . . . 194A.2 Derivation of the Magnetization Jump in the J1-J2 Chain . . . . . . 198Bibliography 201Curriculum Vitae 208.
• Publisher Details: Cham, Switzerland : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 530.12; Quantum theory; Magnetism; Magnetism; Quantum theory; Electronic books
• Languages: English
• ISBNs: 9783030018030; 3030018032
• Related ISBNs: 9783030018023; 3030018024
• Notes: Note: Includes bibliographical references.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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