In addition to equilibrium properties of topologically ordered systems, I 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. Many elastic, thermal, electronic, and magnetic properties of classical glassy material systems are consequences of these materials' being out of equilibrium. Such properties can be tailored according to preparation schemes -- for example, through control of cooling rates. In contrast, because of the difficulties in studying real-time dynamics of strongly interacting quantum systems coupled to a thermal bath, very little is currently known about properties of quantum matter that can be engineered by keeping systems out of equilibrium.

 

I 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.

 

In collaboration with Claudio Castelnovo, Christopher Mudry, and Pierre Pujol, I aso looked at the quantum glassy behavior of a hard constrained spin model in two dimensions that can be mapped into a quantum loop model. This system displays arrested dynamics as it is forced through a quantum phase transition into a phase in a topological sector with only winding loops.

 

Quantum glassiness

Claudio Chamon

C. Castelnovo, C. Chamon, C. Mudry, and P. Pujol