Intermediate magnetization state and competing orders in Dy2Ti2O7 and Ho2Ti2O7.

Among the frustrated magnetic materials, spin-ice stands out as a particularly interesting system. Residual entropy, freezing and glassiness, Kasteleyn transitions and fractionalization of excitations in three dimensions all stem from a simple classical Hamiltonian. But is the usual spin-ice Hamiltonian a correct description of the experimental systems? Here we address this issue by measuring magnetic susceptibility in the two most studied spin-ice compounds, Dy2Ti2O7 and Ho2Ti2O7, using a vector magnet. Using these results, and guided by a theoretical analysis of possible distortions to the pyrochlore lattice, we construct an effective Hamiltonian and explore it using Monte Carlo simulations. We show how this Hamiltonian reproduces the experimental results, including the formation of a phase of intermediate polarization, and gives important information about the possible ground state of real spin-ice systems. Our work suggests an unusual situation in which distortions might contribute to the preservation rather than relief of the effects of frustration.

Statistical transmutation in doped quantum dimer models.

We prove a "statistical transmutation" symmetry of doped quantum dimer models on the square, triangular, and kagome lattices: the energy spectrum is invariant under a simultaneous change of statistics (i.e., bosonic into fermionic or vice versa) of the holes and of the signs of all the dimer resonance loops. This exact transformation enables us to define the duality equivalence between doped quantum dimer Hamiltonians and provides the analytic framework to analyze dynamical statistical transmutations. We investigate numerically the doping of the triangular quantum dimer model with special focus on the topological Z(2) dimer liquid. Doping leads to four (instead of two for the square lattice) inequivalent families of Hamiltonians. Competition between phase separation, superfluidity, supersolidity, and fermionic phases is investigated in the four families.

Magnetization plateaus induced by a coupling to the lattice.

We present a novel mechanism for the appearance of magnetization plateaus in quasi-one-dimensional quantum spin systems, which is induced by the coupling to the underlying lattice. We investigate in detail a simple model of a frustrated spin-1/2 Heisenberg chain coupled to adiabatic phonons under an external magnetic field, but the present mechanism is expected to be more general. Using field theoretic methods complemented by extensive density matrix renormalization group techniques, we show that magnetization plateaus at nontrivial rational values of the magnetization can be stabilized by the lattice coupling. We suggest that such a scenario could be relevant for some low dimensional frustrated spin-Peierls compounds.