Transitions in and out of quantum topological phases
Some strongly correlated quantum many body systems display a type of order which cannot be characterized by any local order parameter. Instead, as proposed by Xiao-Gang Wen, such order is topological in nature, with the fractional quantum Hall systems being the primary example so far: they are liquid states that exhibit exotic properties such as a ground state (GS) degeneracy that cannot be lifted by any local perturbations and fractionalized degrees of freedom. Topologically ordered states are also interesting in that their robustness against local perturbations might be of use for decoherence-free quantum computation.
My research on topologically ordered systems is directed at understanding the phase transitions that can occur and that take systems into and out of topological phases. We have investigated the issue of fragility of topological phases to thermal fluctuations, which tend to destroy the order for infinitesimal temperature in two dimensional systems, if the thermodynamic limit is taken first. We have also constructed quantum Hamiltonians for which the ground state is known exactly as a function of a parameter that takes the system across a zero-temperature quantum phase transition, thus allowing the characterization of the topological state near the quantum critical point.
We have also shown that it is possible to extend the notion of topological order to classical systems. The counterpart of the ground state degeneracy in the quantum systems is that the phase space of configurations in the classical system is disconnected (thus leading to broken ergodicity). Such classical topological order occurs in classical systems subjected to hard constraints.
Topological order and topological entropy in classical systems
Claudio Castelnovo and Claudio Chamon,
Phys. Rev. B 76, 174416 (2007)
Entanglement and topological entropy of the toric code at finite temperature
Claudio Castelnovo and Claudio Chamon,
Phys. Rev. B 76, 184442 (2007)
A quantum topological phase transition at the microscopic level
Claudio Castelnovo and Claudio Chamon,
Phys. Rev. B 77, 054433 (2008)
Topological order in a 3D toric code at finite temperature
Claudio Castelnovo and Claudio Chamon,
Phys. Rev. B 78, 155120 (2008)
Toric-boson model: Toward a topological quantum memory at finite temperature
A. Hamma, C. Castelnovo, and C. Chamon,
Phys. Rev. B 86, 165133 (2012)