Abstract
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 in order 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 $20 \times 20$ 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 $\mathbb{Z}_3$ 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.
Highlights
Gauge theories are of paramount importance in fundamental physics
Starting from periodic Gaussian states introduced in Ref. [52], we extend the variational wave function to have an imaginary part to account for real-time dynamics
We introduce a class of variational states, complex periodic Gaussian states, to study ground-state properties and real-time dynamics in a (2 + 1)-dimensional U (1) lattice gauge theory
Summary
Gauge theories are of paramount importance in fundamental physics. Its most prominent example, the standard model of particle physics, describes electromagnetic, weak, and strong interactions. It has been shown that these Hamiltonians or truncations [12] thereof can be mapped to Hamiltonians of quantum devices (e.g., ultracold atoms, trapped ions, or superconducting qubits) to study such theories by quantum simulation [13,14,15,16] Another option is to study the Hamiltonian by designing appropriate variational ansatz states which are both efficiently tractable and capture the most relevant features of the theory. To access physics difficult to simulate with Monte Carlo simulation of Euclidean lattice gauge theories, we study ground-state properties and nonequilibrium physics, namely, real-time dynamics after a quantum quench.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
