One dimensional staggered bosons, clock models, and their noninvertible symmetries

Journal Article · 16 September 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.054508 · OSTI ID:2473946

Berenstein, David ; Lloyd, P. N. Thomas

We study systems of staggered boson Hamiltonians in a one dimensional lattice and in particular how the translation symmetry by one unit in these systems is in reality a noninvertible symmetry closely related to T-duality. We also study the simplest systems of clock models derived from these staggered boson Hamiltonians. We show that the noninvertible symmetries of these lattice models together with the discrete ${\mathbb{Z}}_N$ symmetry predict that these are critical points with a $U\left(1\right)$ current algebra at $c=1$ and radius $\sqrt{2N}$ whenever $N>4$ . We also present an independent computation of this value that arises directly from the staggered boson variables and does not use these additional symmetries. We also present a theoretical estimate of the values of critical coupling constants away from the self-dual symmetry point in these clock models. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0019139
• OSTI ID: 2473946
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 5 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English