# Supersolid phases of Rydberg-excited bosons on a triangular lattice

## TL;DR

This paper explores the phase diagram of Rydberg-excited bosons on a triangular lattice, revealing various supersolid phases and providing insights for experimental realization, with notable differences from square lattice behavior.

## Contribution

It presents the first detailed numerical study of supersolid phases of Rydberg bosons on a triangular lattice, highlighting unique phase behaviors and proposing experimental parameters.

## Key findings

- Identification of multiple supersolid phases on a triangular lattice.
- Absence of checkerboard supersolid and superfluid-to-supersolid transition on the triangular lattice.
- Comparison showing qualitative similarities and key differences with square lattice results.

## Abstract

Recent experiments with ultracold Rydberg-excited atoms have shown that long-range interactions can give rise to spatially ordered structures. Observation of crystalline phases in a system with Rydberg atoms loaded into an optical lattice seems also within reach. Here we investigate a bosonic model on a triangular lattice suitable for description of such experiments. Numerical simulations based on bosonic dynamical mean-field theory reveal a rich phase diagram with different supersolid phases. Comparison with the results obtained for a square lattice geometry shows qualitatively similar results in a wide range of parameters, however, on a triangular lattice we do not observe the checkerboard supersolid. Moreover, unlike on a square lattice we did not find a phase transition from uniform superfluid to supersolid induced by increase of the hopping amplitude on a triangular lattice. Based on our results we propose an intuitive interpretation of the nature of different supersolid phases. We also propose parameters for the experimental realization.