Entanglement Smectic and Stripe Order

Spontaneous symmetry breaking and more recently entanglement are two cornerstones of quantum matter. We introduce the notion of anisotropic entanglement ordered phases, where the spatial profile of spin-pseudospin entanglement spontaneously lowers the fourfold rotational symmetry of the underlying crystal to a twofold one, while the charge density retains the full symmetry. The resulting phases, which we term entanglement smectic and entanglement stripe, exhibit a rich Goldstone mode spectrum and a set of phase transitions as a function of underlying anisotropies. We discuss experimental consequences of such anisotropic entanglement phases distinguishing them from more conventional charge or spin stripes. Our discussion of this interplay between entanglement and spontaneous symmetry breaking focuses on multicomponent quantum Hall systems realizing textured Wigner crystals, as may occur in graphene or possibly also in moiré systems, highlighting the rich landscape and properties of possible entanglement ordered phases.