Resonating valence bond liquid physics on the triangular lattice

We give an account of the short-range RVB liquid phase on the triangular lattice, starting from an elementary introduction to quantum dimer models including details of the overlap expansion used to generate them. The fate of the topological degeneracy of the state under duality is discussed, as well as recent developments including its possible relevance for quantum computing.Comment: Invited talk at Yukawa Institute Workshop on Quantum Spin Systems; Review with further details for Phys. Rev. Lett 86, 1881 (2001); to appear in Progr. Theor. Phys. (includes relevant style files

From exotic phases to microscopic Hamiltonians

We report recent analytical progress in the quest for spin models realising exotic phases. We focus on the question of `reverse-engineering' a local, SU(2) invariant S=1/2 Hamiltonian to exhibit phases predicted on the basis of effective models, such as large-N or quantum dimer models. This aim is to provide a point-of-principle demonstration of the possibility of constructing such microscopic lattice Hamiltonians, as well as to complement and guide numerical (and experimental) approaches to the same question. In particular, we demonstrate how to utilise peturbed Klein Hamiltonians to generate effective quantum dimer models. These models use local multi-spin interactions and, to obtain a controlled theory, a decoration procedure involving the insertion of Majumdar-Ghosh chainlets on the bonds of the lattice. The phases we thus realise include deconfined resonating valence bond liquids, a devil's staircase of interleaved phases which exhibits Cantor deconfinement, as well as a three-dimensional U(1) liquid phase exhibiting photonic excitations.Comment: Invited talk at Peyresq Workshop on "Effective models for low-dimensional strongly correlated systems". Proceedings to be published by AIP. v2: references adde

Hydrogenic states of monopoles in diluted quantum spin ice

We consider the effect of adding quantum dynamics to a classical topological spin liquid, with particular view to how best to detect its presence in experiment. For the Coulomb phase of spin ice, we find quantum effects to be most visible in the gauge-charged monopole excitations. In the presence of weak dilution with nonmagnetic ions we find a particularly crisp phenomenon, namely the emergence of hydrogenic excited states in which a magnetic monopole is bound to a vacancy at various distances. Via a mapping to an analytically tractable single particle problem on the Bethe lattice, we obtain an approximate expression for the dynamic neutron scattering structure factor.Comment: 4 pages, 4 figures; supplemental material: 3 pages, 2 figure

Semiclassical degeneracies and ordering for highly frustrated magnets in a field

We discuss ground state selection by quantum fluctuations in frustrated magnets in a strong magnetic field. We show that there exist dynamical symmetries -- one a generalisation of Henley's gauge-like symmetry for collinear spins, the other the quantum relict of non-collinear weathervane modes -- which ensure a partial survival of the classical degeneracies. We illustrate these for the case of the kagome magnet, where we find zero-point energy differences to be rather small everywhere except near the collinear `up-up-down` configurations, where there is rotational but not translational symmetry breaking. In the effective Hamiltonian, we demonstrate the presence of a term sensitive to a topological `flux'. We discuss the connection of such problems to gauge theories by casting the frustrated lattices as medial lattices of appropriately chosen simplex lattices, and in particular we show how the magnetic field can be used to tune the physical sector of the resulting gauge theories.Comment: 10 pages, 8 figure