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Abstract:

We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as $\ell(ω)\sim 1/ω^α$. We show that the well known result $α=2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $α$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $α=1$. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.

Abstract:

Certain classical statistical systems with strong local constraints are known to exhibit Coulomb phases, where long-range correlation functions have power-law forms. Continuous transitions from these into ordered phases cannot be described by a naive application of the Landau-Ginzburg-Wilson theory, since neither phase is thermally disordered. We present an alternative approach to a critical theory for such systems, based on a mapping to a quantum problem in one fewer spatial dimensions. We apply this method to spin ice, a magnetic material with geometrical frustration, which exhibits a Coulomb phase and a continuous transition to an ordered state in the presence of a magnetic field applied in the [100] direction.

Abstract:

We study geometrically frustrated antiferromagnets with magnetoelastic coupling. Frustration in these systems may be relieved by a structural transition to a low temperature phase with reduced lattice symmetry. We examine the statistical mechanics of this transition and the effects on it of quenched disorder, using Monte Carlo simulations of the classical Heisenberg model on the pyrochlore lattice with coupling to uniform lattice distortions. The model has a transition between a cubic, paramagnetic high-temperature phase and a tetragonal, Neel ordered low-temperature phase. It does not support the spin-Peierls phase, which is predicted as an additional possibility within Landau theory, and the transition is first-order for reasons unconnected with the symmetry analysis of Landau theory. Quenched disorder stabilises the cubic phase, and we find a phase diagram as a function of temperature and disorder strength similar to that observed in ZnCdCrO.