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 Transitionsorganizes 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.
Table of Contents
NEW DIRECTIONS AND NEW CONCEPTS IN QUANTUM PHASE TRANSITIONS
Finite Temperature Dissipation and Transport Near Quantum Critical Points, Subir Sachdev
Dissipation, Quantum Phase Transitions, and Measurement, Sudip Chakravarty
Universal Dynamics Near Quantum Critical Points, Anatoli Polkovnikov and Vladimir Gritsev
Fractionalization and Topological Order, Masaki Oshikawa
Entanglement Renormalization: An Introduction, Guifré Vidal
The Geometry of Quantum Phase Transitions, Gerardo Ortiz
PROGRESS IN MODEL HAMILTONIANS AND IN SPECIFIC SYSTEMS
Topological Order and Quantum Criticality, Claudio Castelnovo, Simon Trebst, and Matthias Troyer
Quantum Criticality and the Kondo Lattice, Qimiao Si
Spin-Boson Systems: Dissipation and Light Phenomena, Karyn Le Hur
Topological Excitations in Superfluids with Internal Degrees of Freedom, Yuki Kawaguchi and Masahito Ueda
Quantum Monte Carlo Studies of the Attractive Hubbard Hamiltonian, Richard T. Scalettar and George G. Batrouni
Quantum Phase Transitions in Quasi-One-Dimensional Systems, Thierry Giamarchi
Metastable Quantum Phase Transitions in a One-Dimensional Bose Gas, Lincoln D. Carr, Rina Kanamoto, and Masahito Ueda
EXPERIMENTAL REALIZATIONS OF QUANTUM PHASES AND QUANTUM PHASE TRANSITIONS
Quantum Phase Transitions in Quantum Dots, Ileana G. Rau, Sami Amasha, Yuval Oreg, and David Goldhaber-Gordon
Quantum Phase Transitions in Two-Dimensional Electron Systems, Alexander Shashkin and Sergey Kravchenko
Local Observables for QPTs in Strongly Correlated Systems, Eun-Ah Kim, Michael J. Lawler, and J.C. Davis
Molecular Quasi-Triangular Lattice Antiferromagnets, Reizo Kato and Tetsuaki Itou
Quantum Criticality and Superconductivity in Heavy Fermions, Philipp Gegenwart and Frank Steglich
Ultracold Bosonic Atoms in Optical Lattices, Immanuel Bloch
NUMERICAL SOLUTION METHODS FOR QUANTUM PHASE TRANSITIONS Worm Algorithm for Problems of Quantum and Classical Statistics, Nikolay Prokof ’ev and Boris Svistunov
Cluster Monte Carlo Algorithms for Dissipative QPTs, Philipp Werner and Matthias Troyer
Current Trends in Density Matrix Renormalization Group Methods, Ulrich Schollwöck
Simulations based on MPS and PEPS, Valentin Murg, Ignacio Cirac, and Frank Verstraete
Continuous-Time Monte Carlo Methods, Philipp Werner and Andrew J. Millis
QUANTUM PHASE TRANSITIONS ACROSS PHYSICS
Quantum Phase Transitions in Dense QCD, Tetsuo Hatsuda and Kenji Maeda
Quantum Phase Transitions in Coupled Atom-Cavity Systems, Andrew D. Greentree and Lloyd C. L. Hollenberg
Quantum Phase Transitions in Nuclei, Francesco Iachello and Mark A. Caprio
Quantum Critical Dynamics from Black Holes, Sean Hartnoll
Lincoln Carr has produced an epic survey of the current state of knowledge of quantum phase transitions which nicely complements the classic textbook by Subir Sachdev … a thorough overview of methods in current use and recent results.
—Keith Benedict, Contemporary Physics, May 2012
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