Digital lattice gauge theories

TL;DR

This paper introduces a digital scheme for simulating lattice gauge theories with dynamical fermions, using stroboscopic two-body interactions to efficiently realize complex four-body interactions, applicable to various gauge groups and demonstrated with a Z3 model.

Contribution

The authors develop a general digital construction method for lattice gauge theories with dynamical fermions, overcoming previous interaction strength limitations and enabling experimental realization with ultracold atoms.

Findings

Stronger interactions achieved than perturbative methods

Applicable to both Abelian and non-Abelian gauge theories

Demonstrated with a Z3 lattice gauge theory in 2+1 dimensions

Abstract

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.