Understanding Quantum Phase Transitions

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.

NEW DIRECTIONS AND NEW CONCEPTS IN QUANTUM PHASE TRANSITIONS Finite Temperature Dissipation and Transport Near Quantum Critical Points, Subir SachdevDissipation, Quantum Phase Transitions, and Measurement, Sudip ChakravartyUniversal Dynamics Near Quantum Critical Points, Anatoli Polkovnikov and Vladimir GritsevFractionalization and Topological Order, Masaki OshikawaEntanglement Renormalization: An Introduction, Guifré VidalThe Geometry of Quantum Phase Transitions, Gerardo OrtizPROGRESS IN MODEL HAMILTONIANS AND IN SPECIFIC SYSTEMS Topological Order and Quantum Criticality, Claudio Castelnovo, Simon Trebst, and Matthias TroyerQuantum Criticality and the Kondo Lattice, Qimiao SiSpin-Boson Systems: Dissipation and Light Phenomena, Karyn Le HurTopological Excitations in Superfluids with Internal Degrees of Freedom, Yuki Kawaguchi and Masahito UedaQuantum Monte Carlo Studies of the Attractive Hubbard Hamiltonian, Richard T. Scalettar and George G. BatrouniQuantum Phase Transitions in Quasi-One-Dimensional Systems, Thierry GiamarchiMetastable Quantum Phase Transitions in a One-Dimensional Bose Gas, Lincoln D. Carr, Rina Kanamoto, and Masahito UedaEXPERIMENTAL REALIZATIONS OF QUANTUM PHASES AND QUANTUM PHASE TRANSITIONS Quantum Phase Transitions in Quantum Dots, Ileana G. Rau, Sami Amasha, Yuval Oreg, and David Goldhaber-GordonQuantum Phase Transitions in Two-Dimensional Electron Systems, Alexander Shashkin and Sergey KravchenkoLocal Observables for QPTs in Strongly Correlated Systems, Eun-Ah Kim, Michael J. Lawler, and J.C. DavisMolecular Quasi-Triangular Lattice Antiferromagnets, Reizo Kato and Tetsuaki ItouQuantum Criticality and Superconductivity in Heavy Fermions, Philipp Gegenwart and Frank SteglichUltracold Bosonic Atoms in Optical Lattices, Immanuel BlochNUMERICAL SOLUTION METHODS FOR QUANTUM PHASE TRANSITIONS Worm Algorithm for Problems of Quantum and Classical Statistics, Nikolay Prokof ’ev and Boris SvistunovCluster Monte Carlo Algorithms for Dissipative QPTs,Philipp Werner and Matthias TroyerCurrent Trends in Density Matrix Renormalization Group Methods, Ulrich SchollwöckSimulations based on MPS and PEPS, Valentin Murg, Ignacio Cirac, and Frank VerstraeteContinuous-Time Monte Carlo Methods, Philipp Werner and Andrew J. MillisQUANTUM PHASE TRANSITIONS ACROSS PHYSICSQuantum Phase Transitions in Dense QCD, Tetsuo Hatsuda and Kenji MaedaQuantum Phase Transitions in Coupled Atom-Cavity Systems, Andrew D. Greentree and Lloyd C. L. HollenbergQuantum Phase Transitions in Nuclei, Francesco Iachello and Mark A. CaprioQuantum Critical Dynamics from Black Holes, Sean Hartnoll

Lincoln Carr