Quantum Ising phases and transitions in transverse Ising models
The book introduces quantum Ising models and analyses them theoretically and numerically. It discusses both the static and the dynamic behavior of the pure and disordered models, including quantum annealing phenomena. The book consists of eleven chapters. Chapter 1 gives a general introduction to transverse Ising models and their relevance in the context of modeling various quantum order-disorder transitions. In Chapter 2, the energy spectrum of pure transverse Ising chains is discussed. One of the peculiarity of transverse Ising models is the solvability of the pure transverse Ising chain. The exact solution using the Jordan-Wigner transformation is presented. This chapter also includes several numerical analytic methods. In Chapter 3, the Suzuki-Trotter mapping of the \(d\)-dimensional quantum Ising systems to the \((d+1)\)-dimensional classical Ising systems is discussed. Various approximate analytical methods are discussed to study the behavior of the transverse Ising and other generalized models, employing scaling theory and both real space and field theoretical renormalization group techniques. In Chapter 4, the behavior of regularly frustrated transverse Ising systems is discussed. In Chapter 5, the behavior of randomly dilute Ising systems in transverse fields is discussed. Detailed analytical and numerical results revealing the nature of the possible disordered Griffiths phase and its singularities are presented. Chapter 6 presents the behavior of randomly frustrated transverse Ising spin glasses and also of random field transverse Ising models. Chapter 7 discusses the dynamics of quantum transverse Ising models without disorder or frustration and in particular for quenching through the critical point. In Chapter 8, quantum annealing techniques and results are presented. Several analytical results on the bounds of search times and numerical techniques and results for annealing are given. Chapter 9 discusses some applications of tuning quantum fluctuations in some memory models (like the Hopfield model) or in retrieving the patterns with randomly lost information. Chapter 10 discusses how various techniques presented earlier in the book can be translated in order to study the behavior of other quantum mechanical many-body systems. It also discusses the connection of transverse Ising or \(XY\) models with several other well-known old and new models. Chapter 11 gives a brief summary of the book and an outlook.
scientific article; zbMATH DE number 6118251