My collaborators and I have initiated studies of confinement and deconfinement in Yang-Mills theory with the exceptional center-less gauge group G(2) as well as of Sp(N) gauge theories. Michele Pepe and I have observed cascadic decays of strings connecting external charges in higher-dimensional representations. Together with Ferdinando Gliozzi, we have also performed the first precise numerical calculation of the width of Yang-Mills strings, in quantitative agreement with a systematic low-energy effective string theory.
Together with Michael Boegli, Ferenc Niedermayer, and Michele Pepe, we have shown that, despite dislocation lattice artefacts, the vacuum-angle theta makes perfect sense in the 2-d O(3) model. Together with Philippe de Forcrand and Michele Pepe, in analogy to technicolor gauge theories, we have then investigated the slowly walking coupling constant near the conformal fixed point at theta = pi in this model.
My collaborators and I have investigated hole- and electron-doped antiferromagnets by developing systematic low-energy effective field theories, which are a condensed matter analog of baryon chiral perturbation theory in QCD. Using very efficient cluster algorithms, we have determined the low-energy parameters of the effective theories with very high accuracy.
The sign problem hinders progress in understanding many strongly coupled quantum systems. Mattias Troyer and I have shown that some sign problems are NP-hard, and thus practically impossible to solve. This means that no generally applicable method to solve all sign problems can exist. Still, the meron-cluster algorithm, and the more recently developed nested cluster algorithm can be used to either completely solve or at least substantially alleviate very severe sign problems.
Munir Al-Hashimi and I have found some unexpected effects in Quantum mechanics. For example, a particle moving on the surface of a cone may have fractional angular momentum. We have also investigated the spreading of wave packets for particles with an arbitrary energy-momentum dispersion relation, and we have generalized Heisenberg's uncertainty relation to a finite volume of, for example, a quantum dot.