The Localisation Effect

Andrés J. Kálnay

Rebecca Ronke, Marta P. Estarellas, Irene D’Amico +2 more

Anderson localisation is an important phenomenon arising in many areas of physics, and here we explore it in the context of quantum information devices. Finite dimensional spin chains have been demonstrated to be important devices for quantum information transport, and in particular can be engineered to allow for “perfect state transfer” (PST). Here we present extensive investigations of disordered PST spin chains, demonstrating spatial localisation and transport retardation effects, and relate these effects to conventional Anderson localisation. We provide thresholds for Anderson localisation in these finite quantum information systems for both the spatial and the transport domains. Finally, we consider the effect of disorder on the eigenstates and energy spectrum of our Hamiltonian, where results support our conclusions on the presence of Anderson localisation.

Benford Ms

John S. Kimball

A Hubbard model with randomised site energies is used to investigate electron localisation effect associated with both disorder and electron-electron interactions. The ground-state properties of this system are illustrated in a phase diagram. It is shown that electron localisation dominated by interactions is physically distinct from localisation dominated by disorder. Electrons localised through interactions have antiferromagnetic order (at T=0) and electrons localised primarily by disorder have a spin glass magnetic disorder. In this model, true non-magnetic Anderson localisation is a limiting case which applies only for non-interacting electrons.

Leslie Eastman

Luis Antonio González-García, Santiago F. Caballero-Benítez, R. Paredes

We investigate the effects of disorder and lattice geometry against localisation phenomena in a weakly interacting ultracold bosonic gas confined in a 2D optical lattice. The behaviour of the quantum fluid is studied at the mean-field level performing computational experiments, as a function of disorder strength for lattices of sizes similar to current experiments. Quantification of localisation, away from the Bose glass phase, was obtained directly from the stationary density profiles through a robust statistical analysis of the condensate component, as a function of the disorder amplitude. Our results show a smooth transition, or crossover, to localisation induced by disorder in square and triangular lattices. In contrast, associated to its larger tunneling amplitude, honeycomb lattices show absence of localisation for the same range of disorder strengths and same lattice amplitude, while also exhibiting partial localisation for large disorder amplitudes. We also conclude that the coordination number z have a partial influence on how fast this smooth transition occurs as the system size increases. Signatures of disorder are also found in the ground state energy spectrum, where a continuous distribution emerges instead of a distribution of sharp peaks proper to the system in the absence of disorder.