#### 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.