Quantum Phase Transitions.

Sachdev, Subir.

Quantum Phase Transitions. - 2nd ed. - 1 online resource (521 pages)

Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- From the Preface to the first edition -- Acknowledgments -- Preface to the second edition -- Acknowledgments -- Part I: Introduction -- 1 Basic concepts -- 1.1 What is a quantum phase transition? -- 1.2 Nonzero temperature transitions and crossovers -- 1.3 Experimental examples -- 1.4 Theoretical models -- 1.4.1 Quantum Ising model -- 1.4.2 Quantum rotor model -- 1.4.3 Physical realizations of quantum rotors -- 2 Overview -- 2.1 Quantum field theories -- 2.2 What's different about quantum transitions? -- Part II: A first course -- 3 Classical phase transitions -- 3.1 Mean-field theory -- 3.2 Landau theory -- 3.3 Fluctuations and perturbation theory -- 3.3.1 Gaussian integrals -- 3.3.2 Expansion for susceptibility -- Exercises -- 4 The renormalization group -- 4.1 Gaussian theory -- 4.2 Momentum shell RG -- 4.3 Field renormalization -- 4.4 Correlation functions -- Exercises -- 5 The quantum Ising model -- 5.1 Effective Hamiltonian method -- 5.2 Large-g expansion -- 5.2.1 One-particle states -- 5.2.2 Two-particle states -- 5.3 Small-g expansion -- 5.3.1 d=2 -- 5.3.2 d=1 -- 5.4 Review -- 5.5 The classical Ising chain -- 5.5.1 The scaling limit -- 5.5.2 Universality -- 5.5.3 Mapping to a quantum model: Ising spin in a transverse field -- 5.6 Mapping of the quantum Ising chain to a classical Ising model -- Exercises -- 6 The quantum rotor model -- 6.1 Large-g expansion -- 6.2 Small-g expansion -- 6.3 The classical XY chain and an O(2) quantum rotor -- 6.4 The classical Heisenberg chain and an O(3) quantum rotor -- 6.5 Mapping to classical field theories -- 6.6 Spectrum of quantum field theory -- 6.6.1 Paramagnet -- 6.6.2 Quantum critical point -- 6.6.3 Magnetic order -- Exercises -- 7 Correlations, susceptibilities, and the quantum critical point -- 7.1 Spectral representation. 7.1.1 Structure factor -- 7.1.2 Linear response -- 7.2 Correlations across the quantum critical point -- 7.2.1 Paramagnet -- 7.2.2 Quantum critical point -- 7.2.3 Magnetic order -- Exercises -- 8 Broken symmetries -- 8.1 Discrete symmetry and surface tension -- 8.2 Continuous symmetry and the helicity modulus -- 8.2.1 Order parameter correlations -- 8.3 The London equation and the superfluid density -- 8.3.1 The rotor model -- Exercises -- 9 Boson Hubbard model -- 9.1 Mean-field theory -- 9.2 Coherent state path integral -- 9.2.1 Boson coherent states -- 9.3 Continuum quantum field theories -- Exercises -- Part III: Nonzero temperatures -- 10 The Ising chain in a transverse field -- 10.1 Exact spectrum -- 10.2 Continuum theory and scaling transformations -- 10.3 Equal-time correlations of the order parameter -- 10.4 Finite temperature crossovers -- 10.4.1 Low T on the magnetically ordered side,… -- 10.4.2 Low T on the quantum paramagnetic side,… -- 10.4.3 Continuum high T, T >> |Delta| -- 10.4.4 Summary -- 11 Quantum rotor models: large-N limit -- 11.1 Continuum theory and large-N limit -- 11.2 Zero temperature -- 11.2.1 Quantum paramagnet, g>gc -- 11.2.2 Critical point, g=gc -- 11.2.3 Magnetically ordered ground state, g gc , T > Delta+, Delta- -- 11.3.3 Low T on the magnetically ordered side, g < gc, T << Delta- -- 11.4 Numerical studies -- 12 The d = 1, O(N geq 3) rotor models -- 12.1 Scaling analysis at zero temperature -- 12.2 Low-temperature limit of the continuum theory, T << Delta+ -- 12.3 High-temperature limit of the continuum theory, Delta+ << T << J -- 12.3.1 Field-theoretic renormalization group -- 12.3.2 Computation of chi u -- 12.3.3 Dynamics -- 12.4 Summary -- 13 The d = 2, O(N geq 3) rotor models. 13.1 Low T on the magnetically ordered side, T 3 -- 14.3 Order parameter dynamics in d = 2 -- 14.4 Applications and extensions -- 15 Transport in d = 2 -- 15.1 Perturbation theory -- 15.1.1 sigma I -- 15.1.2 sigma II -- 15.2 Collisionless transport equations -- 15.3 Collision-dominated transport -- 15.3.1 epsilon expansion -- 15.3.2 Large-N limit -- 15.4 Physical interpretation -- 15.5 The AdS/CFT correspondence -- 15.5.1 Exact results for quantum critical transport -- 15.5.2 Implications -- 15.6 Applications and extensions -- Part IV: Other models -- 16 Dilute Fermi and Bose gases -- 16.1 The quantum XX model -- 16.2 The dilute spinless Fermi gas -- 16.2.1 Dilute classical gas, kB T 0 -- 16.2.3 High-T limit, kB T >> |mu| -- 16.3 The dilute Bose gas -- 16.3.1 d < 2 -- 16.3.2 d = 3 -- 16.3.3 Correlators of ZB in d = 1 -- Dilute classical gas,… -- Tomonaga-Luttinger liquid,… -- High-T limit,… -- Summary -- 16.4 The dilute spinful Fermi gas: the Feshbach resonance -- 16.4.1 The Fermi-Bose model -- 16.4.2 Large-N expansion -- 16.5 Applications and extensions -- 17 Phase transitions of Dirac fermions -- 17.1 d-wave superconductivity and Dirac fermions -- 17.2 Time-reversal symmetry breaking -- 17.3 Field theory and RG analysis -- 17.4 Ising-nematic ordering. 18 Fermi liquids, and their phase transitions -- 18.1 Fermi liquid theory -- 18.1.1 Independence of choice of vec K0 -- 18.2 Ising-nematic ordering -- 18.2.1 Hertz theory -- 18.2.2 Fate of the fermions -- 18.2.3 Non-Fermi liquid criticality in d = 2 -- Scaling theory -- 18.3 Spin density wave order -- 18.3.1 Mean-field theory -- 18.3.2 Continuum theory -- 18.3.3 Hertz theory -- 18.3.4 Fate of the fermions -- 18.3.5 Critical theory in d = 2 -- 18.4 Nonzero temperature crossovers -- 18.5 Applications and extensions -- 19 Heisenberg spins: ferromagnets and antiferromagnets -- 19.1 Coherent state path integral -- 19.2 Quantized ferromagnets -- 19.3 Antiferromagnets -- 19.3.1 Collinear antiferromagnetism and the quantum nonlinear sigma model -- 19.3.2 Collinear antiferromagnetism in d = 1 -- 19.3.3 Collinear antiferromagnetism in d = 2 -- Antiferromagnets without Berry phases -- Berry phases and valence bond solid order -- 19.3.4 Noncollinear antiferromagnetism in d = 2: deconfined spinons and visons -- 19.3.5 Deconfined criticality -- 19.4 Partial polarization and canted states -- 19.4.1 Quantum paramagnet -- 19.4.2 Quantized ferromagnets -- 19.4.3 Canted and Néel states -- 19.4.4 Zero temperature critical properties -- 19.5 Applications and extensions -- 20 Spin chains: bosonization -- 20.1 The XX chain revisited: bosonization -- 20.2 Phases of H12 -- 20.2.1 Sine-Gordon model -- 20.2.2 Tomonaga-Luttinger liquid -- 20.2.3 Valence bond solid order -- 20.2.4 Néel order -- 20.2.5 Models with SU(2) (Heisenberg) symmetry -- 20.2.6 Critical properties near phase boundaries -- 20.3 O(2) rotor model in d = 1 -- 20.4 Applications and extensions -- 21 Magnetic ordering transitions of disordered systems -- 21.1 Stability of quantum critical points in disordered systems -- 21.2 Griffiths-McCoy singularities -- 21.3 Perturbative field-theoretic analysis. 21.4 Metallic systems -- 21.5 Quantum Ising models near the percolation transition -- 21.5.1 Percolation theory -- 21.5.2 Classical dilute Ising models -- 21.5.3 Quantum dilute Ising models -- 21.6 The disordered quantum Ising chain -- 21.7 Discussion -- 21.8 Applications and extensions -- 22 Quantum spin glasses -- 22.1 The effective action -- 22.1.1 Metallic systems -- 22.2 Mean-field theory -- 22.3 Applications and extensions -- References -- Index.

Updated second edition with several new chapters, for graduates and researchers in condensed matter physics and particle and string theory.

9781139079464


Phase transformations (Statistical physics);Quantum theory.


Electronic books.

QC175.16.P5 S23 2011

530.424