Compact Uk(1) Chern-Simons Theory as a Local Bosonic Lattice Model with Exact Discrete 1-Symmetries

Michael DeMarco and Xiao-Gang Wen
Phys. Rev. Lett. 126, 021603 – Published 13 January 2021
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Abstract

We propose a bosonic Uκ(1) rotor model on a three dimensional spacetime lattice. With the inclusion of a Maxwell term, we show that the low-energy properties of our model can be obtained reliably via a semiclassical approach. Those properties are the same as that of the Chern-Simons field theory, S=d3x(KIJ/4π)AIdAJ. We require the lattice variables on each link to be compact (i.e., take values on circles), which enforces the quantization of the K matrix as a symmetric integer matrix with even diagonals. Our lattice model also has exact 1-symmetries, which gives rise to the 1-form symmetry in the Chern-Simons field theory. In particular, some of those 1-symmetries are anomalous (i.e., non-on-site) in the expected way. The anomaly can be probed via the breaking of those lattice 1-symmetries by the boundaries.

  • Received 17 June 2020
  • Revised 9 October 2020
  • Accepted 20 November 2020

DOI:https://doi.org/10.1103/PhysRevLett.126.021603

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Michael DeMarco* and Xiao-Gang Wen

  • Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • *demarco@mit.edu
  • xgwen@mit.edu

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Issue

Vol. 126, Iss. 2 — 15 January 2021

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