Quantum glassiness
In addition to equilibrium properties of topologically ordered systems, we have also studied non-equilibrium dynamics in a class of topologically ordered systems that have difficulty reaching their quantum ground states if the coupling to the thermal bath is local. The motivation for such studies is the possibility that there are true quantum glasses without quenched disorder.
We have been able to construct concrete examples of solvable models which show without arbitrary or questionable approximations that quantum many-body systems without any disorder and with only local interactions can, indeed, stay out of equilibrium and not reach their ground states as the environment temperature is lowered to absolute zero. These examples, three dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, have topologically ordered ground states but also have slow dynamical relaxation rates akin to those of strong structural glasses.
Quantum glassiness
Claudio Chamon,
Phys. Rev. Lett. 94, 040402 (2005)
Topological Quantum Glassiness
Claudio Castelnovo and Claudio Chamon,
Philosophical Magazine 92, Issue 1-3 (2012)