String Picture for a Model of Frustrated Quantum Magnets and Dimers

We study the effect of quantum dynamics on geometrically frustrated magnets for a transverse field Ising model at finite temperatures. We develop a microscopic derivation of the Landau-Ginzburg-Wilson action for this model and show that it can be interpreted as the free energy of a 3D elastic lattice of noncrossing strings. As a first application, we quantitatively predict the phase diagram and correlations, confirming excellently a key prediction of recent simulations about the existence of unusual phase transitions and an ordered phase. We discuss the implications of our string picture for the understanding of the effect of quenched disorder in such quantum frustrated systems.

Figure 1

(a) Relation between spins and dimers. (b) Vortex-antivortex pair. (c) The two flat states with flippable plaquettes (gray). (d) Mapping of dimers to strings where the numbers denote the height profiles. The string displacement (arrows) is determined by the height of the two plaquettes (gray) which are joined by the displaced dimer.

Figure 2

Phase diagram predicted by Eq. (10) and Monte Carlo results of Fig. 1 in Ref. 6. A critical phase (C) is separated by a boundary at $T_{c,2}$ from the paramagnetic phase (PM) and at $T_{c,1}=4/9T_{c,2}$ from an ordered phase (O).