Studies of Quantum Simulators for Gauge Theories:

In collaboration with Peter Zoller and his group we have constructed quantum simulators for dynamical gauge theories, using ultracold atoms in optical lattices. The gauge fields are represented by quantum links - gauge analogs of quantum spins - which realize continuous gauge invariance with discrete variables in a small Hilbert space that can be represented by discrete states of cold matter. Quantum link models have been developed in collaboration with Shailesh Chandrasekharan.

Studies of Confinement, Deconfinement, and Strings in Lattice Yang-Mills Theory:

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.

Studies of Theta-Vacua and Slowly Walking Couplings in the 2-d O(3) Model:

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.

Studies of Discrete Quantum Systems and Emergent Field Theories:

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.

Studies of the Sign Problem:

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.

Studies of Specific Problems in Quantum Mechanics:

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.