Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

Erez Zohar; Thorsten B. Wahl; Michele Burrello; J. Ignacio Cirac

doi:10.1016/j.aop.2016.08.008

Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

Erez Zohar^*, Thorsten B. Wahl, Michele Burrello, J. Ignacio Cirac

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.

Original language	American English
Pages (from-to)	84-137
Number of pages	54
Journal	Annals of Physics
Volume	374
DOIs	https://doi.org/10.1016/j.aop.2016.08.008
State	Published - 1 Nov 2016
Externally published	Yes

Bibliographical note

Funding Information:
EZ would like to thank the Humboldt foundation for its support. TBW gratefully acknowledges financial support by the Topological Protection and Non-Equilibrium States in Strongly Correlated Electron Systems (TOPNES) (EPSRC grant number EP/I031014/1 ) research programme.

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Lattice gauge theories
Projected Entangled Pair States
Tensor network states

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10.1016/j.aop.2016.08.008

Cite this

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title = "Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study",

abstract = "Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.",

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author = "Erez Zohar and Wahl, {Thorsten B.} and Michele Burrello and Cirac, {J. Ignacio}",

note = "Funding Information: EZ would like to thank the Humboldt foundation for its support. TBW gratefully acknowledges financial support by the Topological Protection and Non-Equilibrium States in Strongly Correlated Electron Systems (TOPNES) (EPSRC grant number EP/I031014/1 ) research programme. Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

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doi = "10.1016/j.aop.2016.08.008",

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AU - Zohar, Erez

AU - Wahl, Thorsten B.

AU - Burrello, Michele

AU - Cirac, J. Ignacio

N1 - Funding Information: EZ would like to thank the Humboldt foundation for its support. TBW gratefully acknowledges financial support by the Topological Protection and Non-Equilibrium States in Strongly Correlated Electron Systems (TOPNES) (EPSRC grant number EP/I031014/1 ) research programme. Publisher Copyright: © 2016 Elsevier Inc.

PY - 2016/11/1

Y1 - 2016/11/1

N2 - Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.

AB - Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.

KW - Lattice gauge theories

KW - Projected Entangled Pair States

KW - Tensor network states

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DO - 10.1016/j.aop.2016.08.008

M3 - Article

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SN - 0003-4916

VL - 374

SP - 84

EP - 137

JO - Annals of Physics

JF - Annals of Physics

ER -

Projected Entangled Pair States with non-Abelian gauge symmetries: An SU(2) study

Abstract

Bibliographical note

Keywords

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