### Abstract

Fundamental forces of Nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such theories describe the dynamics of massless photons and their coupling to matter. However, in two spatial dimension (2D) they are known to exhibit gapped phases at low temperature. In the realm of quantum spin systems, it remains a subject of considerable debate if their low energy physics can be described by emergent gauge degrees of freedom. Here we present a class of simple two-dimensional models that admit a low energy description in terms of an Abelian gauge theory. We find rich phase diagrams for these models comprising exotic deconfined phases and gapless phases - a rare example for 2D Abelian gauge theories. The counter-intuitive presence of gapless phases in 2D results from the emergence of additional symmetry in the models. Moreover, we propose schemes to realize our model with current experiments using ultracold bosonic atoms in optical lattices.

Original language | English |
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Article number | 053608 |

Number of pages | 15 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 95 |

Issue number | 5 |

DOIs | |

Publication status | Published - 4 May 2017 |

### Keywords

- quantum electrodynamics
- Abelian gauge theory
- massless photons
- quantum spin systems
- ultracold bosonic atoms
- gapless phases

## Cite this

Dutta, O., Tagliacozzo, L., Lewenstein, M., & Zakrewski, J. (2017). Toolbox for Abelian lattice gauge theories with synthetic matter.

*Physical Review A - Atomic, Molecular, and Optical Physics*,*95*(5), [053608]. https://doi.org/10.1103/PhysRevA.95.053608