#### ERC Advanced Grant AtomicGaugeSimulator:

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#### Classical and Quantum Simulation of Gauge Theories in Particle and Condensed Matter Physics

Project duration: February 1, 2014 to January 31, 2019

ERC Project Tasks
#### 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 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.