Condensed Matter Theory

Abstract:

We consider the time evolution of observables in the transverse-field Ising chain after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.

Abstract:

We study the physical consequences of site dilution in Kitaev's honeycomb model, in both its gapped and gapless phases. We show that a vacancy binds a flux of the emergent $Z_2$ gauge field and induces a local moment. In the gapped phase this moment is free while in the gapless phase the susceptibility has the dependence $\chi(h)\sim\ln(1/h)$ on field strength $h$. Vacancy moments have interactions that depend on their separation, their relative sublattice, and the phase of the model. Strikingly, in the gapless phase, two nearby vacancies on the same sublattice have a parametrically larger $\chi(h)\sim(h[\ln(1/h)]^{3/2})^{-1}$. In the gapped phase, even a finite density of randomly distributed vacancies remains tractable, via a mapping to a bipartite random hopping problem. This leads to a strong disorder form of the low-energy thermodynamics, with a Dyson-type singularity in the density of states for excitations.

Abstract:

The Pfaffian phase in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing energy is small, i.e., in the weak-coupling, BCS limit, where the coherence length is much larger than the charge screening length. We find that, as in a type I superconductor, vortices attract so that, upon varying the magnetic field from its magic value at ν=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffians exemplify a general dichotomy between type I and type II quantum Hall fluids.

Abstract:

After a long gap following the classic work of Taylor, there have recently been several studies dealing with hydrodynamic synchronization. It is now apparent that synchronization driven by hydrodynamic interactions is not only possible, but relevant to the efficiency of pumping by arrays of cilia and to bacterial swimming. Recent work has included experiments demonstrating synchronization, both in model systems and between bacterial flagella. The effect has been demonstrated in model swimmers and pumps, and large scale simulations have been used to investigate synchronization of cilia and of sperm cells. In this review article, we summarize the various experimental and theoretical studies of hydrodynamic synchronization, and put them in a framework which draws parallels between the different systems and suggests useful directions for further research. © The Royal Society of Chemistry 2011.