Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.
Recenzijos
'This is a very interesting book on the new topic of quantum phase transitions. The book is clearly written and contains an extensive list of references. There have been excellent review articles in the last few years in this area However a well written book like this, which starts from the basic material and reviews in a comprehensive way all the recent literature on the subject, is very useful for both the expert and the newcomer who wants to be introduced into this exciting area. The book is a timely contribution to the research literature and is strongly recommended to all researchers in physics and other related areas.' Dr A. Vourdas, Contemporary Physics 'A huge collection of theoretical observations and experimental facts united in this book by the Quantum Phase Transitions concept makes it attractive for reading.' Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts
Daugiau informacijos
The first book to describe the theory of quantum phase transitions in condensed matter systems.
Preface xi Acknowledgments xv Part I: Introduction 1(36) Basic Concepts 3(10) What Is a Quantum Phase Transition? 3(2) Quantum Versus Classical Phase Transitions 5(1) Experimental Examples 6(2) Theoretical Models 8(5) Quantum Ising Model 8(2) Quantum Rotor Model 10(3) The Mapping to Classical Statistical Mechanics: Single-Site Models 13(15) The Classical Ising Chain 13(7) The Scaling Limit 16(1) Universality 17(1) Mapping to a Quantum Model: Ising Spin in a Transverse Field 18(2) The Classical X Y Chain and an O(2) Quantum Rotor 20(6) The Classical Heisenberg Chain and an O(3) Quantum Rotor 26(2) Overview 28(9) Quantum Field Theories 30(3) Whats Different about Quantum Transitions? 33(4) Part II: Quantum Ising and Rotor Models 37(154) The Ising Chain in a Transverse Field 39(39) Limiting Cases at T=0 41(5) Strong Coupling, g ≫ 1 42(3) Weak Coupling, g ≪ 1 45(1) Exact Spectrum 46(3) Continuum Theory and Scaling Transformations 49(5) Equal-Time Correlations of the Order Parameter 54(3) Finite-Temperature Crossovers 57(20) Low T on the Magnetically Ordered Side, Δ > 0, T ≪ Δ 59(6) Low T on the Quantum Paramagnetic Side, Δ < 0, T ≪ |Δ| 65(4) Continuum High T, T ≫ |Δ| 69(6) Summary 75(2) Applications and Extensions 77(1) Quantum Rotor Models: Large-N Limit 78(23) Limiting Cases 79(4) Strong Coupling, g ≫ 1 80(2) Weak Coupling, g ≪ 1 82(1) Continuum Theory and Large-N Limit 83(2) Zero Temperature 85(6) Quantum Paramagnet, g > gc 86(1) Critical Point, g = gc 87(2) Magnetically Ordered Ground State, g < gc 89(2) Nonzero Temperatures 91(8) Low T on the Quantum Paramagnetic Side, g > gc, T ≪ Δ+ 96(1) High T, T ≫ Δ+, Δ- 97(1) Low T on the Magnetically Ordered Side, g < gc, T ≪ Δ- 97(2) Applications and Extensions 99(2) The d = 1, O(N ≤ 3) Rotor Models 101(22) Scaling Analysis at Zero Temperature 103(1) Low-Temperature Limit of Continuum Theory, T ≪ Δ+ 104(6) High-Temperature Limit of Continuum Theory, Δ+ ≪ T ≪ J 110(11) Field-Theoretic Renormalization Group 112(3) Computation of Xu 115(1) Dynamics 116(5) Summary 121(1) Applications and Extensions 121(2) The d = 2, O(N ≤ 3) Rotor Models 123(22) Low T on the Magnetically Ordered Side, T ≪ ρs 125(9) Computation of ξc 126(3) Computation of τϕ 129(2) Structure of Correlations 131(3) Dynamics of the Quantum Paramagnetic and High-T Regions 134(9) Zero Temperature 136(4) Nonzero Temperatures 140(3) Summary 143(1) Applications and Extensions 144(1) Physics Close to and above the Upper-Critical Dimension 145(23) Zero Temperature 147(4) Perturbation Theory 147(2) Tricritical Crossovers 149(1) Field-Theoretic Renormalization Group 150(1) Statics at Nonzero Temperatures 151(8) d < 3 153(4) d > 3 157(2) Order Parameter Dynamics in d = 2 159(6) Applications and Extensions 165(3) Transport in d = 2 168(23) Perturbation Theory 172(4) σI 175(1) σII 176(1) Collisionless Transport Equations 176(4) Collision-Dominated Transport 180(8) &epsis; Expansion 180(5) Large-N Limit 185(3) Physical Interpretation 188(1) Applications and Extensions 189(2) Part III: Other Models 191(144) Boson Hubbard Model 193(10) Mean-Field Theory 195(3) Continuum Quantum Field Theories 198(3) Applications and Extensions 201(2) Dilute Fermi and Bose Gases 203(26) The Quantum X X Model 205(2) The Dilute Spinless Fermi Gas 207(7) Dilute Classical Gas, T ≪ |μ|, μ < 0 209(1) Fermi Liquid, kBT ≪ μ, μ > 0 210(3) High-T Limit, T ≫ |μ| 213(1) The Dilute Bose Gas 214(8) d < 2 216(2) d = 3 218(4) Correlators of ZB in d = 1 222(6) Dilute Classical Gas, T ≪ |μ|, μ < 0 223(2) Tomonaga-Luttinger Liquid, T ≪ μ, μ > 0 225(1) High-T Limit, T ≫ |μ| 226(1) Summary 227(1) Applications and Extensions 228(1) Phase Transitions of Fermi Liquids 229(11) Effective Field Theory 230(4) Finite-Temperature Crossovers 234(4) Applications and Extensions 238(2) Heisenberg Spins: Ferromagnets and Antiferromagnets 240(34) Coherent State Path Integral 240(5) Quantized Ferromagnets 245(5) Antiferromagnets 250(15) Collinear Order 251(9) Noncollinear Ordering and Deconfined Spinons 260(5) Partial Polarization and Canted States 265(7) Quantum Paramagnet 267(1) Quantized Ferromagnets 268(1) Canted and Neel States 268(2) Zero Temperature Critical Properties 270(2) Applications and Extensions 272(2) Spin Chains: Bosonization 274(24) The X X Chain Revisited: Bosonization 275(8) Phases of H12 283(12) Sine--Gordon Model 286(1) Tomonaga-Luttinger Liquid 287(1) Spin-Peierls Order 288(3) Neel Order 291(1) Models with SU (2) (Heisenberg) Symmetry 292(2) Critical Properties near Phase Boundaries 294(1) O(2) Rotor Model in d = 1 295(1) Applications and Extensions 296(2) Magnetic Ordering Transitions of Disordered Systems 298(22) T. Senthil Stability of Quantum Critical Points in Disordered Systems 299(1) Griffiths--McCoy Singularities 300(3) Perturbative Field-Theoretic Analysis 303(3) Metallic Systems 305(1) Quantum Ising Models Near the Percolation Transition 306(5) Percolation Theory 306(1) Classical Dilute Ising Models 307(1) Quantum Dilute Ising Models 308(3) The Disordered Quantum Ising Chain 311(7) Discussion 318(1) Applications and Extensions 319(1) Quantum Spin Glasses 320(15) The Effective Action 321(5) Metallic Systems 325(1) Mean-Field Theory 326(7) Applications and Extensions 333(2) References 335(14) Index 349
