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A classification of invertible phases of bosonic quantum lattice systems in one dimension

Kapustin, Anton and Sopenko, Nikita and Yang, Bowen (2021) A classification of invertible phases of bosonic quantum lattice systems in one dimension. Journal of Mathematical Physics, 62 (8). Art. No. 081901. ISSN 0022-2488. doi:10.1063/5.0055996. https://resolver.caltech.edu/CaltechAUTHORS:20210301-154744254

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Abstract

We study invertible states of 1D bosonic quantum lattice systems. We show that every invertible 1D state is in a trivial phase: after tensoring with some unentangled ancillas, it can be disentangled by a fuzzy analog of a finite-depth quantum circuit. If an invertible state has symmetries, it may be impossible to disentangle it in a way that preserves the symmetries, even after adding unentagled ancillas. We show that in the case of a finite unitary symmetry G, the only obstruction is an index valued in degree-2 cohomology of G. We show that two invertible G-invariant states are in the same phase if and only if their indices coincide.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/5.0055996DOIArticle
https://arxiv.org/abs/2012.15491arXivDiscussion Paper
ORCID:
AuthorORCID
Kapustin, Anton0000-0003-3903-5158
Sopenko, Nikita0000-0002-8479-1924
Yang, Bowen0000-0003-4778-831X
Alternate Title:A classification of phases of bosonic quantum lattice systems in one dimension
Additional Information:© 2021 Published under an exclusive license by AIP Publishing. Submitted: 5 May 2021; Accepted: 25 July 2021; Published Online: 11 August 2021. We would like to thank P. Etingof and B. Simon for advice. We are also grateful to Y. Ogata for drawing our attention to an error in Lemma 4.1 in the original version of this paper. This research was supported, in part, by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632. A.K. was also supported by the Simons Investigator Award. B.Y. acknowledges the Caltech mathematics department for a graduate fellowship awarded in fall 2020.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Caltech Division of Physics, Mathematics and AstronomyUNSPECIFIED
Issue or Number:8
DOI:10.1063/5.0055996
Record Number:CaltechAUTHORS:20210301-154744254
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210301-154744254
Official Citation:A classification of invertible phases of bosonic quantum lattice systems in one dimension. J. Math. Phys. 62, 081901 (2021); doi: 10.1063/5.0055996
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108260
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Mar 2021 00:24
Last Modified:12 Aug 2021 20:47

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