Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-06-14
J. Stat. Phys. 116, 755 (2004)
Physics
Condensed Matter
Statistical Mechanics
5 pages, 2 postscript figures automatically included
Scientific paper
We study quantum antiferromagnetism on the highly frustrated checkerboard lattice, also known as the square lattice with crossings. The quantum Heisenberg antiferromagnet on this lattice is of interest as a two-dimensional analog of the pyrochlore lattice magnet. By combining several approaches we conclude that this system is most likely ordered for all values of spin, $S$, with a Neel state for large $S$ giving way to a two-fold degenerate valence-bond solid for smaller $S$. We show next that the Ising antiferromagnet with a weak four-spin exchange, equivalent to square ice with the leading quantum dynamics, exhibits long range ``anti-ferroelectric'' order. As a byproduct of this analysis we obtain, in the system of weakly coupled ice planes, a sliding phase with XY symmetry.
Moessner Richhild
Sondhi Shivaji L.
Tchernyshyov Oleg
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