Anderson localisation in tight-binding models with flat bands

We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localised nor spatially extended. Further, we establish a mapping between this localisation problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.Comment: 5 pages, 3 figures, as published (this version includes minor corrections

On the origin of surface states in a correlated local-moment film

The electronic quasiparticle structure of a ferromagnetic local moment film is investigated within the framework of the s-f model. For the special case of a single electron in an otherwise empty energy band being exchange coupled to a fully ordered localised spin system the problem can be solved exactly and, for the spin-down electron, some marked correlation effects can be found. We extend our model to incorporate the influence of the surface on the electronic structure. Therefore we modify the hopping integrals in the vicinity of the surface. This leads to the existence of surface states, both for the spin-up and the spin-down spectral density of states. The interplay between the modification of the hopping integrals and the existence of surface states and correlation effects is discussed in detail.Comment: 9 pages, 9 figures, accepted for publication in European Physical Journal

Ferromagnetic spin-polaron on complex lattices

We present a simpler derivation of the exact solution of a spin-polaron in a ferromagnet and generalize it to complex lattices and/or longer range exchange interactions. As a specific example, we analyze a two-dimensional MnO$_2$-like lattice (as in the ferromagnetic layers in LaMnO$_3$) and discuss the properties of the resulting spin-polaron in various regimes. At strong couplings the solution is reminiscent of the Zhang-Rice singlet, however the electronic wavefunction involved in the singlet is dependent on the momentum of the singlet, and multiple bands may appear.Comment: 12 pages, 7 figure

A Diabatic Surface Hopping Algorithm based on Time Dependent Perturbation Theory and Semiclassical Analysis

Surface hopping algorithms are popular tools to study dynamics of the quantum-classical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representations, based on time dependent perturbation theory and semiclassical analysis. The algorithm can be viewed as a Monte Carlo sampling algorithm on the semiclassical path space for piecewise deterministic path with stochastic jumps between the energy surfaces. The algorithm is validated numerically and it shows good performance in both weak coupling and avoided crossing regimes

Finite-momentum Bose-Einstein condensates in shaken 2D square optical lattices

We consider ultracold bosons in a 2D square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. It is therefore necessary to account for higher-order hopping terms, which are renormalized differently by the shaking, and introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates, with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott-insulator and the different superfluid phases, and present the time-of-flight images expected to be observed experimentally. Our results open up new possibilities for the realization of bosonic analogs of the FFLO phase describing inhomogeneous superconductivity.Comment: 7 pages, 7 figure