Talks

Calculating universal properties of quantum phase transitions in microscopic Hamiltonians is a challenging task, made possible through large-scale numerical simulations coupled with finite-size scaling analyses. The continuing advancement of quantum Monte Carlo technologies, together with modern high-performance computing infrastructure, has made amenable a new class of quantum Heisenberg Hamiltonian with four-spin exchange, which may harbor a continuous Néel-to-Valence Bond Solid quantum phase transition. Such an exotic quantum critical point would necessarily lie outside of the standard Landau-Ginzburg-Wilson paradigm, and may contain novel physical phenomena such as emergent topological order and quantum number fractionalization. I will discuss efforts to calculate universal critical exponents using large-scale quantum Monte Carlo simulations, and compare them to theoretical predictions, in particular from the recent theory of deconfined quantum criticality.

Responding electrically to magnetic stimuli and vise versa, multiferroics offer exciting possibilities for applications and challenge our understanding of coupled lattice and spin degrees of freedom in solids. I discuss how multiferroic properties can develop in frustrated magnets where competing interactions produce non-collinear spin order and symmetry breaking lattice distortions. Our experiments in TbMnO3, Ni3V2O8, and RbFe(MoO4)2 show that when the low temperature magnetic order breaks spatial inversion symmetry it is accompanied by ferroelectricity [1-3]. Conversely, the application of an electric field favors one of the two inversion symmetry related antiferromagnetic domains. We infer that inversion symmetry breaking magnetic order acts as an effective electric field through magneto-elastic distortions that relieve frustration. We also present evidence for microscopic correspondence between the ferroelectric and the antiferromagnetic domain structure. The results presented are based on magnetic neutron diffraction, pyrocurrent measurements, and theoretical work by A. B. Harris [4]. [1] M. Kenzelmann, A. B. Harris, S. Jonas, C. Broholm, J. Schefer, S. B. Kim, C. L. Zhang, S.-W. Cheong, O. P. Vajk, and J. W. Lynn, Phys. Rev. Lett. 95, 087206 (2005). [2] G. Lawes, A. B. Harris, T. Kimura, N. Rogado, R. J. Cava, A. Aharony, O. Entin-Wohlman, T. Yildirim, M. Kenzelmann, C. Broholm, and A. P. Ramirez, Phys. Rev. Lett. 95, 087205 (2005). [3] M. Kenzelmann, G. Lawes, A.B. Harris, G. Gasparovic, C. Broholm, A.P. Ramirez, G.A. Jorge, M. Jaime, S. Park, Q. Huang, A.Ya. Shapiro, and L.A. Demianets, Phys. Rev. Lett. 98, 267205 (2007). [4] A. B. Harris, Phys. Rev. B 76 , 054447 (2007).

We analyze the trans-Planckian problem and its formulation in the context of cosmology, black-hole physics, and analogue models of gravity. In particular, we discuss the phenomenological approach to the trans-Planckian problem based on modified, locally Lorentz-breaking, dispersion relations (MDR). The main question is whether MDR leave an detectable imprint on macroscopic physics. In the framework of the semi-classical theory of gravity, this question can be unambiguously answered only through a rigorous formulation of quantum field theory on curved space with MDR. In this context, we propose a momentum-space analysis of the Green\'s function, which will hopefully lead to the correct renormalization of the stress tensor.

Motivated by recent observations of superfluidity of ultracold fermions in optical lattices, we investigate the stability of superfluid flow of paired fermions in the lowest band of a strong optical lattice. For fillings close to one fermion per site, we show that superflow breaks down via a dynamical instability leading to a transient density wave. At lower fillings, there is a distinct dynamical instability, where the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. Our most interesting finding is the existence of a transition, over a range of fillings close to one fermion per site, from the fermion depairing instability to the density wave instability as the strength of the pairing interaction is increased. By sharp contrast, the ground state in this regime evolves smoothly with increasing interaction analogous to the BCS-BEC crossover.

I present a short review of recent developments both in experiment and theory in Quantum Hall Effect in Graphene. The emphasis is on the interpretation of the dynamics underlying recently experimentally discovered novel plateaus in strong magnetic fields (B > 20 T).

URu2Si2 is a moderate heavy fermion system which undergoes two transitions with decreasing temperature. The lower transition (1.5K) is to a possibly unconventional superconducting state, whereas the nature of the upper transition (17.5K) is poorly understood. Large lambda-like anomalies are seen in specific heat, along with strong signatures in other transport measurements such as resistivity and magnetic susceptibility. Neutron diffraction measurements only detect a very small ordered moment (0.03 μB), which is too small to give such large bulk signatures. This has prompted theorists to propose various exotic mechanisms to explain this so-called hidden order. I will review our group\'s efforts to understand this system, including our results on non-linear susceptibility and muon spin relaxation under hydrostatic pressure, as well as inelastic neutron scattering studies of this system.

I will discuss the interplay between the fermionic nodal quasiparticles of a d-wave superconductor and the various spin and charge orders that have been observed in the cuprate superconductors. Fluctuations of a composite \'nematic\' order are identified as the dominant source of inelastic scattering which broadens the quasiparticle spectral function.

I will describe antiferromagnets and superconductors near quantum phase transitions. There is a remarkable analogy between their dynamics and the holographic description of Hawking radiation from black holes. I will show how insights from this analogy have shed light on experiments on the cuprate high temperature superconductors.

I will show how to construct very general ERG equations, and will use this as the starting point for a discussion of Polchinski\'s equation and its cousins. I will introduce diagrammatics and an associated universal calculus, which will be illustrated with a simple calculation.

The dynamics of particles moving in a medium defined by its relativistically invariant stochastic properties is investigated. For this aim, the force exerted on the particles by the medium is defined by a stationary random variable as a function of the proper time of the particles. The equations of motion for a single one-dimensional particle are obtained and numerically solved. A conservation law for the drift momentum of the particle during its random motion is shown. Moreover, the conservation of the mean value of the total linear momentum for two particles repelling each other according to the Coulomb interaction also follows. Therefore, the results indicate the realization of a kind of stochastic Noether theorem in the system under study.