TY - JOUR
T1 - Fermionic projected entangled pair states and local U(1) gauge theories
AU - Zohar, Erez
AU - Burrello, Michele
AU - Wahl, Thorsten B.
AU - Cirac, J. Ignacio
PY - 2015/12/1
Y1 - 2015/12/1
N2 - 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 this
work, we introduce a way to extend the set of symmetric PEPS in order to
include local gauge invariance and investigate lattice gauge theories
with fermionic matter. To this purpose, we provide as a case study and
first example, the construction of a fermionic PEPS, based on Gaussian
schemes, invariant under both global and local U(1) gauge
transformations. The obtained states correspond to a truncated U(1)
lattice gauge theory in 2+1 dimensions, involving both the gauge field
and fermionic matter. For the global symmetry (pure fermionic) case,
these PEPS can be studied in terms of spinless fermions subject to a
p-wave superconducting pairing. For the local symmetry (fermions and
gauge fields) case, we find confined and deconfined phases in the pure
gauge limit, and we discuss the screening properties of the phases
arising in the presence of dynamical matter.
AB - 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 this
work, we introduce a way to extend the set of symmetric PEPS in order to
include local gauge invariance and investigate lattice gauge theories
with fermionic matter. To this purpose, we provide as a case study and
first example, the construction of a fermionic PEPS, based on Gaussian
schemes, invariant under both global and local U(1) gauge
transformations. The obtained states correspond to a truncated U(1)
lattice gauge theory in 2+1 dimensions, involving both the gauge field
and fermionic matter. For the global symmetry (pure fermionic) case,
these PEPS can be studied in terms of spinless fermions subject to a
p-wave superconducting pairing. For the local symmetry (fermions and
gauge fields) case, we find confined and deconfined phases in the pure
gauge limit, and we discuss the screening properties of the phases
arising in the presence of dynamical matter.
KW - Tensor network states
KW - Projected entangled pair states
KW - Lattice gauge theories
U2 - 10.1016/j.aop.2015.10.009
DO - 10.1016/j.aop.2015.10.009
M3 - Journal article
SN - 0003-4916
VL - 363
SP - 385
EP - 439
JO - Annals of Physics
JF - Annals of Physics
ER -