Magnetic Field Effects in Low-Dimensional Quantum Magnets
著者
書誌事項
Magnetic Field Effects in Low-Dimensional Quantum Magnets
(Springer theses : recognizing outstanding Ph. D. research)
Springer, c2018
大学図書館所蔵 全2件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Doctoral thesis accepted by Boston University, MA, USA
Includes bibriographical references
内容説明・目次
内容説明
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.
目次
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
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