Two-Dimensional Quantum XY Model with Ring Exchange and External Field

We present the zero-temperature phase diagram of a square lattice quantum spin 1/2 XY model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the XY-order, striped or valence bond solid, staggered Neel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.Comment: 4 pages, 4 figure

Anisotropic Release of the Residual Zero-point Entropy in the Spin Ice Compound Dy2Ti2O7: Kagome-ice Behavior

We report the specific heat and entropy of single crystals of the spin ice compound Dy2Ti2O7 at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions: [100], [110], [111] and [112]. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches Rln2. However, in the intermediate field region, the entropy in fields along the [111] direction is different from those for the other three field directions. For the [111] direction the frustration structure changes from that of three-dimensional(3D) pyrochlore to that of two-dimensional(2D) Kagome-like lattice with constraint due to the ice rule, leading to different values of zero-point entropy.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.Comment: 14 pages, 8 figure

Condensed matter and AdS/CFT

I review two classes of strong coupling problems in condensed matter physics, and describe insights gained by application of the AdS/CFT correspondence. The first class concerns non-zero temperature dynamics and transport in the vicinity of quantum critical points described by relativistic field theories. I describe how relativistic structures arise in models of physical interest, present results for their quantum critical crossover functions and magneto-thermoelectric hydrodynamics. The second class concerns symmetry breaking transitions of two-dimensional systems in the presence of gapless electronic excitations at isolated points or along lines (i.e. Fermi surfaces) in the Brillouin zone. I describe the scaling structure of a recent theory of the Ising-nematic transition in metals, and discuss its possible connection to theories of Fermi surfaces obtained from simple AdS duals.Comment: 39 pages, 12 figures; Lectures at the 5th Aegean summer school, "From gravity to thermal gauge theories: the AdS/CFT correspondence", and the De Sitter Lecture Series in Theoretical Physics 2009, University of Groninge