  One scenario for the non-classical moment of inertia of solid He-4 discovered
by Kim and Chan [Nature 427, 225 (2004)] is the superfluidity of
micro-crystallite interfaces. On the basis of the most simple model of a
quantum crystal--the checkerboard lattice solid--we show that the superfluidity
of interfaces between solid domains can exist in a wide range of parameters. At
strong enough inter-particle interaction, a superfluid interface becomes an
insulator via a quantum phase transition. Under the conditions of particle-hole
symmetry, the transition is of the standard U(1) universality class in 3D,
while in 2D the onset of superfluidity is accompanied by the interface
roughening, driven by fractionally charged topological excitations.
