Valence-bond crystal in a {111} slice of the pyrochlore antiferromagnet

摘要: We investigate theoretically the ordering effect of quantum spin fluctuations in a Heisenberg antiferromagnet on two-dimensional network corner-sharing tetrahedra. This is obtained as ${111}$ slice highly frustrated pyrochlore lattice, from which it inherits equivalence all three pairs opposite bonds each tetrahedron. The lowest-order (in $1∕S$) corrections partially lift huge degeneracy classical ground state and select an ensemble states with long-range valence-bond order.