In this area, our main work is on Quantum Antiferromagnets
using variational Monte Carlo,
and the Handscomb method, a less well-known quantum Monte Carlo method.
See: "The spin-1/2 Heisenberg Antiferromagnet on the Square Lattice and its application to cuprous oxides"
E. Manousakis, Rev. Mod. Phys. 63, 1 (1991).
Equilibrium Critical Phenomena have been extensively studied by a number
of numerical methods.
Critical dynamics, dymanical critical exponents, and finite-size scaling of transport properties
are by far less well studied. The main reason is that to simulate real time dynamics requires
large computational resources and, thus, one was limited by small size lattices.
Recent algorithmic advances and the fact that we can now built our own
massively parallel cluster with high perfomance to cost ratio enable us to perform
calculations to calculate critical dynamical properties.
Quantum Hall Effect
We have recently carried out Monte Carlo simulation studies of a model
we believe might describe the recently observed anisotropic response
in quantum hall systems.
See: E. Fradkin et al, Phys. Rev. Lett. 84, 1982 (2000).