Symmetry Classes of Open Fermionic Quantum Matter

We present a full symmetry classification of fermion matter in and out of thermal equilibrium. Our approach starts from first principles, the ten different classes of linear and antilinear state transformations in fermionic Fock spaces, and symmetries defined via invariance properties of the dynamic...

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Autores principales:	Alexander Altland, Michael Fleischhauer, Sebastian Diehl
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/5e59e533defe4f318ef6e5749e08e823
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spelling	oai:doaj.org-article:5e59e533defe4f318ef6e5749e08e8232021-12-02T17:16:23ZSymmetry Classes of Open Fermionic Quantum Matter10.1103/PhysRevX.11.0210372160-3308https://doaj.org/article/5e59e533defe4f318ef6e5749e08e8232021-05-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.11.021037http://doi.org/10.1103/PhysRevX.11.021037https://doaj.org/toc/2160-3308We present a full symmetry classification of fermion matter in and out of thermal equilibrium. Our approach starts from first principles, the ten different classes of linear and antilinear state transformations in fermionic Fock spaces, and symmetries defined via invariance properties of the dynamical equation for the density matrix. The object of classification is then the generators of reversible dynamics, dissipation and fluctuations, featuring’ in the generally irreversible and interacting dynamical equations. A sharp distinction between the symmetries of equilibrium and out-of-equilibrium dynamics, respectively, arises from the different role played by “time” in these two cases: In unitary quantum mechanics as well as in “microreversible” thermal equilibrium, antilinear transformations combined with an inversion of time define time-reversal symmetry. However, out of equilibrium an inversion of time becomes meaningless, while antilinear transformations in Fock space remain physically significant, and hence must be considered in autonomy. The practical consequence of this dichotomy is a novel realization of antilinear symmetries (six out of the ten fundamental classes) in nonequilibrium quantum dynamics that is fundamentally different from the established rules of thermal equilibrium. At large times, the dynamical generators thus symmetry classified determine the steady-state nonequilibrium distributions for arbitrary interacting systems. To illustrate this principle, we consider the fixation of a symmetry protected topological phase in a system of interacting lattice fermions. More generally, we consider the practically important class of mean field interacting systems, represented by Gaussian states. This class is naturally described in the language of non-Hermitian matrices, which allows us to compare to previous classification schemes in the literature.Alexander AltlandMichael FleischhauerSebastian DiehlAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 11, Iss 2, p 021037 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Alexander Altland Michael Fleischhauer Sebastian Diehl Symmetry Classes of Open Fermionic Quantum Matter
description	We present a full symmetry classification of fermion matter in and out of thermal equilibrium. Our approach starts from first principles, the ten different classes of linear and antilinear state transformations in fermionic Fock spaces, and symmetries defined via invariance properties of the dynamical equation for the density matrix. The object of classification is then the generators of reversible dynamics, dissipation and fluctuations, featuring’ in the generally irreversible and interacting dynamical equations. A sharp distinction between the symmetries of equilibrium and out-of-equilibrium dynamics, respectively, arises from the different role played by “time” in these two cases: In unitary quantum mechanics as well as in “microreversible” thermal equilibrium, antilinear transformations combined with an inversion of time define time-reversal symmetry. However, out of equilibrium an inversion of time becomes meaningless, while antilinear transformations in Fock space remain physically significant, and hence must be considered in autonomy. The practical consequence of this dichotomy is a novel realization of antilinear symmetries (six out of the ten fundamental classes) in nonequilibrium quantum dynamics that is fundamentally different from the established rules of thermal equilibrium. At large times, the dynamical generators thus symmetry classified determine the steady-state nonequilibrium distributions for arbitrary interacting systems. To illustrate this principle, we consider the fixation of a symmetry protected topological phase in a system of interacting lattice fermions. More generally, we consider the practically important class of mean field interacting systems, represented by Gaussian states. This class is naturally described in the language of non-Hermitian matrices, which allows us to compare to previous classification schemes in the literature.
format	article
author	Alexander Altland Michael Fleischhauer Sebastian Diehl
author_facet	Alexander Altland Michael Fleischhauer Sebastian Diehl
author_sort	Alexander Altland
title	Symmetry Classes of Open Fermionic Quantum Matter
title_short	Symmetry Classes of Open Fermionic Quantum Matter
title_full	Symmetry Classes of Open Fermionic Quantum Matter
title_fullStr	Symmetry Classes of Open Fermionic Quantum Matter
title_full_unstemmed	Symmetry Classes of Open Fermionic Quantum Matter
title_sort	symmetry classes of open fermionic quantum matter
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/5e59e533defe4f318ef6e5749e08e823
work_keys_str_mv	AT alexanderaltland symmetryclassesofopenfermionicquantummatter AT michaelfleischhauer symmetryclassesofopenfermionicquantummatter AT sebastiandiehl symmetryclassesofopenfermionicquantummatter
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Symmetry Classes of Open Fermionic Quantum Matter

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