Lecturer: Dr. Erez Zohar
Affiliation: Max Planck Institute of Quantum Optics
Abstract:
Tensor networks, and in particular
Projected Entangled Pair States
(PEPS), are a powerful tool for the
study of quantum many body physics,
thanks to both their built-in ability of
classifying and studying symmetries,
and the efficient numerical
calculations they allow. In the work I
will present, we introduced a way to
extend the set of symmetric PEPS in
order to include local gauge
invariance and investigate lattice
gauge theories with fermionic matter
[1].
I will review the basic ingredients of
PEPS and the way of handling global
symmetries with them, and show how
to gauge them and make the
symmetry local [2]. As an example, I
will present our construction of
fermionic PEPS, based on Gaussian
schemes, invariant under both global
and local U(1) gauge transformations.
The obtained states describe a
truncated U(1) lattice gauge theory [3]
in 2+1 dimensions, involving both the
gauge field and fermionic matter; I
will present the methods which
enabled us to study these states, and
the results in which some well-known
physical phases were identified (e.g.
confinement of static charges and
screening of dynamical ones).
[1] Fermionic projected entangled
pair states and local U(1) gauge
theories, EZ, M. Burrello, T. B. Wahl
and J. I. Cirac, Ann. Phys. 363, 385
(2015).
[2] Building Projected Entangled Pair
States with a Local Gauge Symmetry.
EZ and M. Burrello,
arxiv:1511.08426.
[3] Formulation of lattice gauge
theories for quantum simulations, EZ
and M. Burrello, Phys. Rev. D 91,
054506 (2015).