We review recent theoretical and experimental efforts aimed at the investigation of the physics of interacting disordered bosons (so-called dirty bosons) in the context of quantum magnetism. The physics of dirty bosons is relevant to a wide variety o
f condensed matter systems, encompassing Helium in porous media, granular superconductors and ultracold atoms in disordered optical potentials, to cite a few. Nevertheless, the understanding of the transition from a localized, Bose-glass phase to an ordered, superfluid condensate phase still represents a fundamentally open problem. Still to be constructed is also a quantitative description of the highly inhomogeneous and strongly correlated phases connected by the transition. We discuss how disordered magnetic insulators in a strong magnetic field can provide a well controlled realization of the above transition. Combining numerical simulations with experiments on real materials can shed light on some fundamental properties of the critical behavior, such as the scaling of the critical temperature to condensation close to the quantum critical point.
The strong-leg S=1/2 Heisenberg spin ladder system (C7H10N)2CuBr4 is investigated using Density Matrix Renormalization Group (DMRG) calculations, inelastic neutron scattering, and bulk magneto-thermodynamic measurements. Measurements showed qualitati
ve differences compared to the strong-rung case. A long-lived two-triplon bound state is confirmed to persist across most of the Brillouin zone in zero field. In applied fields, in the Tomonaga-Luttinger spin liquid phase, elementary excitations are attractive, rather than repulsive. In the presence of weak inter-ladder interactions, the strong-leg system is considerably more prone to 3-dimensional ordering.
Inelastic neutron scattering is used to measure spin excitations in fully deuterated single crystal samples of the strong-leg antiferromagnetic S=1/2 spin ladder compound (C$_7$H$_{10}$N)$_2$CuBr$_4$. Sharp resolution-limited magnons are observed acr
oss the entire one-dimensional Brillouin zone. The results validate the previously proposed {it symmetric} spin ladder model and provide a reliable estimate of the relevant exchange interactions.
Temperature dependencies of gap energies and magnon lifetimes are measured in the quasi-1-dimensional S=1/2 gapped quantum magnets IPA-CuCl3 and Sul-Cu2Cl4 using inelastic neutron scattering. The results are compared to those found in literature for
S=1 Haldane spin chain materials and to theoretical calculations for the O(3)- and O(N)- quantum non-linear sigma-models. It is found that when the T=0 energy gap Delta is used as the temperature scale, all experimental and theoretical curves are identical to within system-dependent but temperature-independent scaling factors of the order of unity. This quasi-universality extends over a surprising broad T range, at least up to kappa T ~ 1.5 Delta.
Inelastic and elastic neutron scattering is used to study spin correlations in the quasi-one dimensional quantum antiferromagnet IPA-CuCl3 in strong applied magnetic fields. A condensation of magnons and commensurate transverse long-range ordering is
observe at a critical filed $H_c=9.5$ T. The field dependencies of the energies and polarizations of all magnon branches are investigated both below and above the transition point. Their dispersion is measured across the entire 1D Brillouin zone in magnetic fields up to 14 T. The critical wave vector of magnon spectrum truncation [Masuda et al., Phys. Rev. Lett. 96, 047210 (2006)] is found to shift from h_c 0.35 at H>H_c. A drastic reduction of magnon bandwidths in the ordered phase [Garlea et al., Phys. Rev. Lett. 98, 167202 (2007)] is observed and studied in detail. New features of the spectrum, presumably related to this bandwidth collapse, are observed just above the transition field.
