Real-time dynamics in 2+1D compact QED using complex periodic Gaussian states

Julian Bender*, Patrick Emonts, Erez Zohar, J. Ignacio Cirac

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We introduce a class of variational states to study ground-state properties and real-time dynamics in (2+1)-dimensional compact QED. These are based on complex Gaussian states which are made periodic to account for the compact nature of the U(1) gauge field. Since the evaluation of expectation values involves infinite sums, we present an approximation scheme for the whole variational manifold. We calculate the ground-state energy density for lattice sizes up to 20×20 and extrapolate to the thermodynamic limit for the whole coupling region. Additionally, we study the string tension both by fitting the potential between two static charges and by fitting the exponential decay of spatial Wilson loops. As the ansatz does not require a truncation in the local Hilbert spaces, we analyze truncation effects which are present in other approaches. The variational states are benchmarked against exact solutions known for the one plaquette case and exact diagonalization results for a Z3 lattice gauge theory. Using the time-dependent variational principle, we study real-time dynamics after various global quenches, e.g., the time evolution of a strongly confined electric field between two charges after a quench to the weak-coupling regime. Up to the points where finite-size effects start to play a role, we observe equilibrating behavior.

Original languageAmerican English
Article number043145
JournalPhysical Review Research
Issue number4
StatePublished - 27 Oct 2020

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© 2020 authors. Published by the American Physical Society.


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