Bikas K. Chakrabarti

Phase Transitions in Disordered Quantum Systems: Transverse Ising Models

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