Magnetic frustration commonly leads, in two-dimensional (2D)
quantum spin systems,
to the (dynamical) formation of spin singlets or dimers.
Generically, systems of quantum fluctuating dimers may
order into Valence Bond Crystals (VBC) or
remain in some unconventional quantum dimer liquid
similar to Anderson's original RVB state
The two-dimensional Quantum Dimer Model (QDM) plays
an increasing role (Ref. 1) in the understanding of frustrated
quantum antiferromagnets and quantum-disordered spin systems
and offers completely new routes of investigations.
In addition, little is known theoretically on itinerant frustrated systems
and the investigation of doped
quantum dimer models is also a promising
route towards a better understanding of e.g. doped frustrated antiferromagnets
or the pseudogap phase of the high-T$_c$ cuprates.
I will review here recent progress on simulations
of quantum dimer models, both relevant for undoped and doped Mott insulators or RVB magnets under magnetic fields. Green Function Monte Carlo
are shown to be very efficient to simulate QDM whenever Peron-Frobenius theorem applies (Refs. 2,3,4). For example a new phase has been recently discovered in the undoped case on the square lattice (Ref. 3). However, I shall argue that a proper modeling of hole-doped Mott insulators leads to a minus-sign problem. In that case, Lanczos exact diagonalisations can provide useful insights in the physics of the
model (Ref. 5).
1. D.S. Rokhsar and S.A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988).
2. O.F. Syljuasen, Phys. Rev. B 71, 020401(R) (2005); R. Moessner and S. L. Sondhi,
Phys. Rev. B 63, 224401 (2001).
3. A. Ralko, D. Poilblanc and R. Moessner, Phys. Rev. Lett. 100, 037201 (2008).
4. A. Ralko, F. Mila and D. Poilblanc, Phys. Rev. Lett. 99, 127202 (2007);
A. Ralko, F. Becca and D. Poilblanc, Phys. Rev. Lett. 101, 117204 (2008).
5. D. Poilblanc, Phys. Rev. Lett. 100, 157206 (2008).