Continuous symmetry breaking in a two-dimensional Rydberg array

Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions(1-3). The nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry leads to the emergence of gapless Goldstone modes controlling, for instance, the thermodynamic stability of the ordered phase(4,5). Here, we realize a two-dimensional dipolar XY model that shows a continuous spin-rotational symmetry using a programmable Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of a long-range XY order, a feature prohibited in the absence of long-range dipolar interaction. Our exploration of the many-body physics of XY interactions complements recent works using the Rydberg-blockade mechanism to realize Ising-type interactions showing discrete spin rotation symmetry(6-9).

Automated summary

Spontaneous symmetry breaking is the basis of classifying phases of matter and their transitions, and continuous symmetry breaking leads to the emergence of gapless Goldstone modes that control the thermodynamic stability of the ordered phase. In this study, a two-dimensional dipolar XY model is realized using a programmable Rydberg quantum simulator, and the presence of long-range XY order is characterized. This work complements recent studies on Ising-type interactions showing discrete spin rotation symmetry using the Rydberg-blockade mechanism.