Correlated partial disorder in a weakly frustrated quantum antiferromagnet

Partial disorder --the microscopic coexistence of long-range magnetic order and disorder-- is a rare phenomenon, that has been experimental and theoretically reported in some Ising- or easy plane-spin systems, driven by entropic effects at finite temperatures. Here, we present an analytical and numerical analysis of the $S=1/2$ Heisenberg antiferromagnet on the $\sqrt{3}\times \sqrt{3}$-distorted triangular lattice, which shows that its quantum ground state has partial disorder in the weakly frustrated regime. This state has a 180$^\circ$ N\'eel ordered honeycomb subsystem, coexisting with disordered spins at the hexagon center sites. These central spins are ferromagnetically aligned at short distances, as a consequence of a Casimir-like effect originated by the zero-point quantum fluctuations of the honeycomb lattice.