Disordered flat bands on the kagome lattice

We study two models of correlated bond- and site-disorder on the kagome lattice considering both translationally invariant and completely disordered systems. The models are shown to exhibit a perfectly flat ground state band in the presence of disorder for which we provide exact analytic solutions. Whereas in one model the flat band remains gapped and touches the dispersive band, the other model has a finite gap, demonstrating that the band touching is not protected by topology alone. Our model also displays fully saturated ferromagnetic groundstates in the presence of repulsive interactions, an example of disordered flat band ferromagnetism.Comment: 7+3 pages, 4+2 figures, accepted versio

Temperature dependence of butterfly effect in a classical many-body system

We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterise many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered correlator. Due to the emergence of a spin liquid phase, the chaotic dynamics extends all the way to zero temperature. We thus determine the full temperature dependence of two complementary aspects of the butterfly effect: the Lyapunov exponent, $\mu$, and the butterfly speed, $v_b$, and study their interrelations with usual measures of spin dynamics such as the spin-diffusion constant, $D$ and spin-autocorrelation time, $\tau$. We find that they all exhibit power law behaviour at low temperature, consistent with scaling of the form $D\sim v_b^2/\mu$ and $\tau^{-1}\sim T$. The vanishing of $\mu\sim T^{0.48}$ is parametrically slower than that of the corresponding quantum bound, $\mu\sim T$, raising interesting questions regarding the semi-classical limit of such spin systems.Comment: 6+4 pages, 4+8 figures, ancillary files include videos of the dynamic

Synthetic dimensions in the strong-coupling limit: Supersolids and pair superfluids

We study the many-body phases of bosonic atoms with $N$ internal states confined to a 1D optical lattice under the influence of a synthetic magnetic field and strong repulsive interactions. The $N$ internal states of the atoms are coupled via Raman transitions creating the synthetic magnetic field in the space of internal spin states corresponding to recent experimental realisations. We focus on the case of strong \mbox{SU}(N) invariant local density-density interactions in which each site of the 1D lattice is at most singly occupied, and strong Raman coupling, in distinction to previous work which has focused on the weak Raman coupling case. This allows us to keep only a single state per site and derive a low energy effective spin $1/2$ model. The effective model contains first-order nearest neighbour tunnelling terms, and second-order nearest neighbour interactions and correlated next-nearest neighbour tunnelling terms. By adjusting the flux $\phi$ one can tune the relative importance of first-order and second-order terms in the effective Hamiltonian. In particular, first-order terms can be set to zero, realising a novel model with dominant second-order terms. We show that the resulting competition between density-dependent tunnelling and repulsive density-density interaction leads to an interesting phase diagram including a phase with long-ranged pair-superfluid correlations. The method can be straightforwardly extended to higher dimensions and lattices of arbitrary geometry including geometrically frustrated lattices where the interplay of frustration, interactions and kinetic terms is expected to lead to even richer physics.Engineering and Physical Sciences Research Council (Grant ID: EP/K030094/1)This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevA.94.02363

Scattering theory for Floquet-Bloch states

Motivated by recent experimental implementations of artificial gauge fields for gases of cold atoms, we study the scattering properties of particles that are subjected to time-periodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the single-particle dynamics can be described in terms of spatially extended Floquet-Bloch waves. We develop a general formalism for the scattering of these Floquet-Bloch waves. An important role is played by the conservation of Floquet quasi-energy, which is defined only up to the addition of integer multiples of $\hbar\omega$ for a Hamiltonian with period $T=2\pi/\omega$. We discuss the consequences of this for the interpretation of "elastic" and "inelastic" scattering in cases of physical interest. We illustrate our general results with applications to: the scattering of a single particle in a Floquet-Bloch state from a static potential; and, the scattering of two particles in Floquet-Bloch states through their interparticle interaction. We analyse examples of these scattering processes that are closely related to the schemes used to general artifical gauge fields in cold-atom experiments, through optical dressing of internal states, or through time-periodic modulations of tight-binding lattices. We show that the effects of scattering cannot, in general, be understood by an effective time-independent Hamiltonian, even in the limit $\omega \to \infty$ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stablize many-body phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in current experimental set-up can be switched off by additional confinement of transverse motion.This work was supported by EPSRC Grant No. EP/K030094/1.This is the accepted manuscript of a paper published in Physical Review A (Bilitewski T, Cooper NR, Physical Review A 2015, 91, 033601, doi:10.1103/PhysRevA.91.033601). The final version is available at http://dx.doi.org/10.1103/PhysRevA.91.03360

Population dynamics in a Floquet realization of the Harper-Hofstadter Hamiltonian

We study the recent Floquet-realisation of the Harper-Hofstadter model in a gas of cold bosonic atoms. We study in detail the scattering processes in this system in the weakly interacting regime due to the interplay of particle interactions and the explicit time dependence of the Floquet states that lead to band transitions and heating. We focus on the experimentally used parameters and explicitly model the transverse confining direction. Based on transition rates computed within the Floquet-Fermi golden rule we obtain band population dynamics which are in agreement with the dynamics observed in experiment. Finally, we discuss whether and how photon-assisted collisions that may be the source heating and band population dynamics might be suppressed in the experimental setup by appropriate design of the transverse confining potential. The suppression of such processes will become increasingly important as the experiments progress into simulating strongly interacting systems in the presence of artificial gauge fields.This work was supported by EPSRC Grant No EP/K030094/1.This is the accepted manuscript. The final version is available at http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.063611

Radial flows and angular momentum conservation in galactic chemical evolution

We study the effects of radial flows on Galactic chemical evolution. A simple analytic scheme is developed prescribing the coupling of infall from the intergalactic medium and radial flows within the disc based on angular momentum conservation.Physic

Exotic superconductivity through bosons in a dynamical cluster approximation

We study the instabilities towards (exotic) superconductivity of mixtures of spin-1/2 fermions coupled to scalar bosons on a two-dimensional square lattice with the Dynamical-Cluster-Approximation (DCA) using a numerically exact continuous-time Monte-Carlo solver. The Bogoliubov bosons provide an effective phononic bath for the fermions and induce a non-local retarded interaction between the fermions, which can lead to (exotic) superconductivity. Because of the sign problem the biggest clusters we can study are limited to 2 X 2 in size, but this nevertheless allows us to study the pairing instablilities, and their possible divergence, in the s- and d -wave channels as well as the competition with antiferromagnetic uctuations. At fermionic half-filling we find that d-wave is stable when the mediated interaction by the bosons is of the same order as the bare fermionic repulsion. Its critical temperature can be made as high as the maximum one for s-wave, which opens perspectives for its detection in a cold atom experiment.Physic

Disordered flat bands on the kagome lattice

We study two models of correlated bond- and site-disorder on the kagome lattice considering both translationally invariant and completely disordered systems. The models are shown to exhibit a perfectly at ground state band in the presence of disorder for which we provide exact analytic solutions. Whereas in one model the at band remains gapped and touches the dispersive band, the other model has a finite gap, demonstrating that the band touching is not protected by topology alone. Our model also displays fully saturated ferromagnetic groundstates in the presence of repulsive interactions, an example of disordered at band ferromagnetism.Physic