Quantum magnetism and quantum phase transitions

Abstract:

The frustrated pyrochlore magnet $Yb_{2}Ti_{2}O_{7}$ has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.

Abstract:

The twin discoveries of the quantum Hall effect1, in the 1980s, and of topological band insulators2, in the 2000s, were landmarks in physics that enriched our view of the electronic properties of solids. In a nutshell, these discoveries have tau ght us that quantum mechanical wavefunctions in crystalline solids may carry nontrivial topological invariants which have ramifications for the observable physics. One of the side effects of the recent topological insulator revolution has been that such physics is much more widespread than was appreciated ten years ago. For example, while topological insulators were originally studied in the context of electron wavefunctions, recent work has initiated a hunt for topological insulators in bosonic systems: in photonic crystals3-6, in the vibrational modes of crystals7, and in the excitations of ordered magnets8. Using inelastic neutron scattering along with theoretical calculations, we demonstrate that, in a weak magnetic field, the dimerized quantum magnet SrCu 2 (BO 3 ) 2 is a bosonic topological insulator with topologically protected chiral edge modes of triplon excitations.