Theory seminar: The sign-problem in lattice gauge theory and how to overcome it: A study of (2+1)-dimensional compact quantum electrodynamics

Julian Bender (MPQ)
Following last week’s theory seminar, I will provide some more background on lattice gauge theories and the challenges it faces.

Julian Bender (MPQ)
Group seminar via Zoom
Wed, 9 March 2022, 10:30 (MEZ)

Abstract:

Following last week’s theory seminar, I will provide some more background on lattice gauge theories and the challenges it faces.
The traditional approach towards lattice gauge theories based on Monte-Carlo simulations in the action formalism has been a major success over several decades.
Unfortunately, some theories of interest are affected by the sign-problem which prevents the use of the aforementioned method so that certain questions cannot be addressed (e.g. finite chemical potential scenarios or real-time dynamics).
Based on the Hamiltonian formulation of lattice gauge theory two  methods have recently attracted attention to tackle this problem: the first is based on quantum simulation/quantum computation and the second on variational ansatz states.
While last week’s talk focused on quantum computation, this talk will be focused on a variational method which allows to study, as a first step towards higher-dimensional gauge theories, (2+1)-dimensional compact QED.
The variational ansatz, a combination of neural network inspired ansatz states and a gauge-invariant version of fermionic gaussian states, is evaluated with Monte-Carlo methods but inherently sign-problem free.
To validate the ansatz, it is benchmarked against traditional Monte-Carlo simulations in regimes where the sign problem is absent, in this case two fermion flavors at half-filing. We then study sign-problem affected regimes, e.g. by introducing a non-zero chemical potential.

If you’d like to participate in the seminar, please contact us!