Topological order from quantum loops and nets
Annals of Physics Elsevier 323:12 (2008) 3113-3136
Charge frustration and quantum criticality for strongly correlated fermions.
Physical review letters 101:14 (2008) 146406
Abstract:
We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical result which relates quantum ground states to certain tiling configurations on the square lattice. For periodic boundary conditions this relation implies that the number of ground states grows exponentially with the linear dimensions of the system. We present substantial analytic and numerical evidence that for open boundary conditions the system has gapless edge modes.Critical points in coupled Potts models and critical phases in coupled loop models
Journal of Physics A: Mathematical and Theoretical IOP Publishing 41:21 (2008) 215001
Order parameter statistics in the critical quantum Ising chain.
Physical review letters 100:16 (2008) 165706
Abstract:
The probability distribution of the order parameter is expected to take a universal scaling form at a phase transition. In a spin system at a quantum critical point, this corresponds to universal statistics in the distribution of the total magnetization in the low-lying states. We obtain this scaling function exactly for the ground state and first excited state of the critical quantum Ising spin chain. This is achieved through a remarkable relation to the partition function of the anisotropic Kondo problem, which can be computed by exploiting the integrability of the system.Gauge symmetry and non-Abelian topological sectors in a geometrically constrained model on the honeycomb lattice.
Physical review. E, Statistical, nonlinear, and soft matter physics 75:5 Pt 1 (2007) 051120