Fermionic projected entangled pair states and local U(1) gauge theories

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Fermionic projected entangled pair states and local U(1) gauge theories. / Zohar, Erez; Burrello, Michele; Wahl, Thorsten B.; Cirac, J. Ignacio.

In: Annals of Physics, Vol. 363, 01.12.2015, p. 385-439.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Zohar, E, Burrello, M, Wahl, TB & Cirac, JI 2015, 'Fermionic projected entangled pair states and local U(1) gauge theories', Annals of Physics, vol. 363, pp. 385-439. https://doi.org/10.1016/j.aop.2015.10.009

APA

Zohar, E., Burrello, M., Wahl, T. B., & Cirac, J. I. (2015). Fermionic projected entangled pair states and local U(1) gauge theories. Annals of Physics, 363, 385-439. https://doi.org/10.1016/j.aop.2015.10.009

Vancouver

Zohar E, Burrello M, Wahl TB, Cirac JI. Fermionic projected entangled pair states and local U(1) gauge theories. Annals of Physics. 2015 Dec 1;363:385-439. https://doi.org/10.1016/j.aop.2015.10.009

Author

Zohar, Erez ; Burrello, Michele ; Wahl, Thorsten B. ; Cirac, J. Ignacio. / Fermionic projected entangled pair states and local U(1) gauge theories. In: Annals of Physics. 2015 ; Vol. 363. pp. 385-439.

Bibtex

@article{950c21f9589d42be96252c6725e9f3bc,
title = "Fermionic projected entangled pair states and local U(1) gauge theories",
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 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.",
keywords = "Tensor network states, Projected entangled pair states, Lattice gauge theories",
author = "Erez Zohar and Michele Burrello and Wahl, {Thorsten B.} and Cirac, {J. Ignacio}",
year = "2015",
month = dec,
day = "1",
doi = "10.1016/j.aop.2015.10.009",
language = "English",
volume = "363",
pages = "385--439",
journal = "Annals of Physics",
issn = "0003-4916",
publisher = "Academic Press",

}

RIS

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

VL - 363

SP - 385

EP - 439

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -

ID: 184607152