Ground-state phase diagram of Rydberg atoms in a triangular-prism array

Abstract

We study the ground-state phase diagram of Rydberg atoms in a triangular-prism optical tweezer array using the density matrix renormalization group. By tuning the detuning-to-Rabi-frequency ratio and the Rydberg blockade radius, the system realizes several density-wave phases with spontaneous breaking of translational and leg-exchange symmetries. Unlike two-leg Rydberg ladders with ${\mathbb{Z}}_2$ leg-exchange symmetry, the triangular prism has ${\mathbb{D}}_3$ symmetry, leading to a richer set of ordered phases and transitions. For blockade radius moderately larger than the lattice spacing, a phase with alternating double and single Rydberg occupancy appears at large detuning. It breaks ${\mathbb{Z}}_2$ translational and ${\mathbb{Z}}_3$ rotational symmetry while preserving a rung reflection symmetry. Upon decreasing detuning, it melts through two Berezinskii-Kosterlitz-Thouless transitions with an intermediate critical phase described by a ${\mathbb{Z}}_6$ clock model. At larger blockade radius, a phase with one Rydberg excitation per triangle and broken ${\mathbb{D}}_3$ symmetry appears through a first-order transition. When double occupation of neighboring triangles is suppressed, rung-trimerized density waves develop as detuning increases from the disordered phase. Their melting follows the same structure as in Rydberg chains and two-leg ladders: the ${\mathbb{Z}}_2$ case has Ising critical lines, while the ${\mathbb{Z}}_3$ and ${\mathbb{Z}}_4$ cases have chiral critical lines, with Potts and Ashkin-Teller points only on the corresponding commensurate lines. Inside the ${\mathbb{Z}}_2$ rung-trimerized phase, an entanglement-entropy peak signals a crossover regime with enhanced period-2 density modulation before a first-order transition into a ${\mathbb{Z}}_2\times {\mathbb{D}}_3$ phase. Floating phases with incommensurate quasi-long-range order appear between trimerized states of different periods.