Quantum simulation of $\mathbb{Z}_2$ lattice gauge theories with dynamical matter from two-body interactions in $(2+1)$D

17 May 2022  ·  Lukas Homeier, Annabelle Bohrdt, Simon Linsel, Eugene Demler, Jad C. Halimeh, Fabian Grusdt ·

Gauge fields coupled to dynamical matter are a universal framework in many disciplines of physics, ranging from particle to condensed matter physics, but remain poorly understood at strong couplings. Through the steadily increasing control over numerically inaccessible Hilbert spaces, analog quantum simulation platforms have become a powerful tool to study interacting quantum many-body systems. Here we propose a scheme in which a $\mathbb{Z}_2$ gauge structure emerges from local two-body interactions and one-body terms in two spatial dimensions. The scheme is suitable for Rydberg atom arrays and enables the experimental study of both $(2+1)$D $\mathbb{Z}_2$ lattice gauge theories coupled to dynamical matter ($\mathbb{Z}_2$ mLGTs) and quantum dimer models on the honeycomb lattice, for which we derive effective Hamiltonians. We discuss ground-state phase diagrams of the experimentally relevant effective $\mathbb{Z}_2$ mLGT for $U(1)$ and quantum-$\mathbb{Z}_2$ matter featuring deconfined phases. Further, we present realistic experimental probes and show signatures of disorder-free localization as well as the Schwinger effect in $(2+1)$D using small-scale exact diagonalization studies. Our proposed scheme allows to experimentally study not only longstanding goals of theoretical physics, such as Fradkin and Shenker's (PRD 19, 1979) conjectured phase diagram, but also go beyond regimes accessible with current numerical techniques.

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