## Quantum Phase TransitionsDescribing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory. |

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ˆσ analysis antiferromagnets arguments behavior Berry phase boson Chapter classical compute consider continuum theory correlation length coupling crossover cutoff defined density described Dirac fermions discussed in Section dynamic equal-time correlations equation evaluate excitations expansion exponent exponentially expression Fermi liquid Fermi surface fermion ferromagnetic field theory finite fixed point fluctuations free energy frequency ground Hamiltonian interactions invariant Ising chain Ising model large-N lattice leading limit low-energy magnetically ordered mapping matrix mean-field momenta Mott insulator nonzero Note obtain order parameter particles partition function path integral perturbation phase diagram physical precisely properties quantum critical point quantum Ising quantum paramagnetic quantum phase transitions quantum rotor model quasiparticle regime renormalization group rescaling result scaling dimension scaling form scaling function simple singularities spatial spin superfluid susceptibility symmetry temperature thermal transformation universal vanishes zero τϕ φα