Superfluid interfaces in quantum solids

One scenario for the non-classical moment of inertia of solid $^4$He discovered by Kim and Chan [{\it Science}, {\bf 305}, 1941 (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 $d=3 $, while in $d=2$ the onset of superfluidity is accompanied by the interface roughening, driven by fractionally charged topological excitations.