Quantum Spin Glasses

Olivier Parcollet

After two sessions devoted to classical spin glass systems and aging phenomenon, I will talk about quantum spin glasses. Quantum spin glasses have been less studied that their classical analogs, but sometimes quantum effects can not be neglected, mainly around a quantum critical point, when the glass temperature vanishes.

On the theoretical point of view, two extreme limits are useful to study these strongly disordered systems :

1. Models in high dimensions, i.e. mean field, which have been studied statically and recently dynamically, e.g. rotor models or quantum Heisenberg models.
2. Models in low dimension (d=1 in practice), such as the random Ising chain in a transverse magnetic field, where an asymptotically exact renormalisation group procedure has been developed.

I will give some overview over both kind of results, and I will present (as an example) the Heisenberg model in mean field in some details (statics, dynamics, effect of charge degree of freedom). Although this can be a quite technical subject, the emphasis will be on results and general ideas of theoretical methods.