Condensed Matter Theory

Abstract:

We analyse the dynamical response of a range of 3D Kitaev quantum spin-liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines or Weyl points. We find that the behaviour of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a non-vanishing density of states, to the phase shifts encountered in the corresponding X-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine-structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalise, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.

Abstract:

We explore the quantum phase transition between Peierls and charge-density-wave insulating states in the one-dimensional, half-filled, extended Hubbard model with explicit bond dimerization. We show that the critical line of the continuous Ising transition terminates at a tricritical point, belonging to the universality class of the tricritical Ising model with central charge c=7/10. Above this point, the quantum phase transition becomes first order. Employing a numerical matrix-product-state based (infinite) density-matrix renormalization group method we determine the ground-state phase diagram, the spin and two-particle charge excitations gaps, and the entanglement properties of the model with high precision. Performing a bosonization analysis we can derive a field description of the transition region in terms of a triple sine-Gordon model. This allows us to derive field theory predictions for the power-law (exponential) decay of the density-density (spin-spin) and bond-order-wave correlation functions, which are found to be in excellent agreement with our numerical results.

Abstract:

The effects of neighboring droplets on the dissolution of a sessile droplet, i.e. collective effects, are investigated both experimentally and numerically. On the experimental side small approximately 20 nL mono-disperse surface droplets arranged in an ordered pattern were dissolved and their size evolution is studied optically. The droplet dissolution time was studied for various droplet patterns. On the numerical side, lattice-Boltzmann simulations were performed. Both simulations and experiments show that the dissolution time of a droplet placed in the center of a pattern can increase by as much as 60% as compared to a single, isolated droplet, due to the shielding effect of the neighboring droplets. However, the experiments also show that neighboring droplets enhance the buoyancy driven convective flow of the bulk, increasing the mass exchange and counteracting collective effects. We show that this enhanced convection can reduce the dissolution time of droplets at the edges of the pattern to values below that of a single, isolated droplet.

Abstract:

We analyze the dynamical response of a range of three-dimensional Kitaev quantum spin liquids, using lattice models chosen to explore the different possible low-energy spectra for gapless Majorana fermions, with either Fermi surfaces, nodal lines, or Weyl points. We find that the behavior of the dynamical structure factor is distinct in all three cases, reflecting the quasiparticle density of states in two fundamentally different ways. First, the low-energy response is either straightforwardly related to the power with which the low-energy density of states vanishes; or for a nonvanishing density of states, to the phase shifts encountered in the corresponding x-ray edge problem, whose phenomenology we extend to the case of Majorana fermions. Second, at higher energies, there is a rich fine structure, determined by microscopic features of the Majorana spectrum. Our theoretical results test the usefulness of inelastic neutron scattering as a probe of these quantum spin liquids: we find that although spin flips fractionalize, the main features of the dynamical spin response nevertheless admit straightforward interpretations in terms of Majorana and flux loop excitations.