Understanding Quantum Phase Transitions

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Lincoln Carr
CRC Press, 02.11.2010 - 756 Seiten
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Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivity and display fundamental aspects of quantum theory, such as strong correlations and entanglement. Over the last two decades, our understanding of QPTs has increased tremendously due to a plethora of experimental examples, powerful new numerical methods, and novel theoretical understanding of previously intractable quantum many-body problems.

Understanding Quantum Phase Transitions organizes our current understanding of QPTs with an emphasis on examples from condensed matter physics. Bringing together 48 well known physicists involved with the theory and observation of QPTs, this unique work provides a thorough yet concise examination of the field. Each chapter takes readers through past discoveries right up through the latest research results, and then ends with open questions and unsolved problems.

  • Part I treats new concepts and directions in QPTs, from dynamics through dissipation and entanglement, and includes introductory material suitable for scientists new to the field.
  • Part II explores specific models, systems, and aspects of QPTs, including topological order, the Kondo lattice, the Jaynes-Cummings lattice, reduced dimensionality, finite-size effects and metastability, and QPTs in Bose-Einstein condensates.
  • Part III covers experiments motivated by a deeper understanding of QPTs, including quantum dots, 2D electron systems, frustrated lattices in molecular antiferromagnets, heavy fermions, and ultracold atoms in optical lattices.
  • Part IV presents advances in numerical methods used to study QPTs, including cluster Monte Carlo and the worm algorithm, matrix-product-state methods, and dynamical mean-field theory.
  • Part V looks at the relevance of QPTs beyond condensed-matter physics, including their occurrence in neutron stars, the quark-gluon plasma, cavity QED systems, and string theory.

Graduate students, post-doctoral researchers, and professional scientists who seek a deep knowledge of QPTs will all find this book very useful. Researchers in the field will enhance their appreciation of the incredible breadth of the subject in chapters covering material outside their specialties.

 

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Inhalt

Finite Temperature Dissipation andTransport Near Quantum Critical Points
3
Dissipation Quantum Phase Transitionsand Measurement
31
Universal Dynamics Near Quantum Critical Points
59
Fractionalization and Topological Order
91
Entanglement Renormalization An Introduction
115
The Geometry of Quantum Phase Transitions
139
Progress in ModelHamiltonians and in Specific Systems
167
Topological Order and Quantum Criticality
169
Local Observables for Quantum PhaseTransitions in Strongly Correlated Systems
393
Molecular QuasiTriangular Lattice Antiferromagnets
419
Probing Quantum Criticality and itsRelationship with Superconductivity in Heavy Fermions
445
Strong Correlation Effects with UltracoldBosonic Atoms in Optical Lattices
469
Numerical SolutionMethods for Quantum Phase Transitions
497
Worm Algorithm for Problems of Quantumand Classical Statistics
499
Cluster Monte Carlo Algorithms forDissipative Quantum Phase Transitions
523
Current Trends in Density MatrixRenormalization Group Methods
547

Quantum Criticality and the Kondo Lattice
193
Quantum Phase Transitions in SpinBosonSystems Dissipation and Light Phenomena
217
Topological Excitations in Superfluids withInternal Degrees of Freedom
241
Quantum Monte Carlo Studies of theAttractive Hubbard Hamiltonian
265
Quantum Phase Transitions inQuasiOneDimensional Systems
289
Metastable Quantum Phase Transitions in aOneDimensional Bose Gas
311
Experimental Realizationsof Quantum Phases andQuantum Phase Transitions
339
Quantum Phase Transitions in Quantum Dots
341
Quantum Phase Transitions inTwoDimensional Electron Systems
369
Simulations Based on Matrix Product Statesand Projected Entangled Pair States
571
ContinuousTime Monte Carlo Methods forQuantum Impurity Problems and DynamicalMean Field Calculations
597
Quantum PhaseTransitions Across Physics
621
Quantum Phase Transitions in Dense QCD
623
Quantum Phase Transitions in CoupledAtomCavity Systems
647
Quantum Phase Transitions in Nuclei
673
Quantum Critical Dynamics from Black Holes
701
Back Cover
725
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