Phase Transition in Disordered Quantum Systems: Transverse Ising Models

We introduce the transverse Ising model as a prototype for discussing quantum phase transition. Mean field theory, application to superconductivity by BCS and real space renormalization group technique (in one dimension) are discussed. Next we introduce Suzuki-Trotter formalism to show the correspondence between d-dimensional quantum system with a (d + 1)-dimensional classical system. We then discuss transverse Ising spin glass models, namely S-K model, E-A model, and the ±J model with Ising spin in transverse field. We briefly discuss the mean field, exact diagonalization, and quantum Monte Carlo results for their phase diagrams. Next we discuss the question of replica symmetry restoration in quantum spin glasses (due to tunnelling possibility through the barriers). Then we discuss the quantum annealing technique and indicate its relationship with replica symmetry restoration in quantum spin glasses.