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Exact bosonization in two spatial dimensions and a new class of lattice gauge theories

Chen, Yu-An and Kapustin, Anton and Radičević, Đorđe (2018) Exact bosonization in two spatial dimensions and a new class of lattice gauge theories. Annals of Physics, 393 . pp. 234-253. ISSN 0003-4916. https://resolver.caltech.edu/CaltechAUTHORS:20180412-112218749

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Abstract

We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contain Chern–Simons-like terms. Finally, we write down a fermionic dual of the gauged Ising model (the Fradkin-Shenker model).


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.aop.2018.03.024DOIArticle
https://www.sciencedirect.com/science/article/pii/S0003491618300873PublisherArticle
https://arxiv.org/abs/1711.00515arXivDiscussion Paper
ORCID:
AuthorORCID
Chen, Yu-An0000-0002-8810-9355
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2018 Elsevier Inc. Received 1 March 2018, Accepted 30 March 2018, Available online 11 April 2018. A. K. would like to thank T. Senthil for a discussion. The research of A. K. and Y. C. was supported in part by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number de-sc0011632. A. K. was also supported by the Simons Investigator Award. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation.
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Simons FoundationUNSPECIFIED
Industry CanadaUNSPECIFIED
Ontario Ministry of Economic Development and InnovationUNSPECIFIED
Subject Keywords:Bosonization; Lattice gauge theory; Spin systems
Record Number:CaltechAUTHORS:20180412-112218749
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180412-112218749
Official Citation:Yu-An Chen, Anton Kapustin, Đorđe Radičević, Exact bosonization in two spatial dimensions and a new class of lattice gauge theories, Annals of Physics, Volume 393, 2018, Pages 234-253, ISSN 0003-4916, https://doi.org/10.1016/j.aop.2018.03.024. (http://www.sciencedirect.com/science/article/pii/S0003491618300873)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85783
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:12 Apr 2018 20:55
Last Modified:16 Dec 2019 20:41

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