Disorder and transport in the topological insulators

Alexander Dauphin

Université Libre de Bruxelles

The search for novel topological phase of matter has attracted much interest during the last decades. The quest for these fascinating quantum states, whose properties are guaranteed by topological invariants, finds its origin in the discovery of the quantum Hall effect. The latter takes place in two-dimensional electron gases subjected to very high magnetic fields. In quantum Hall systems, external magnetic fields break time-reversal symmetry and lead to quantized transverse conductivity, whose associated current is carried by chiral edge- states. More recently, time-reversal invariant topological insulators have been observed in quantum wells and are characterized by robust spin-transport.

In this talk, I will present several methods to calculate the Hall conductivity of a quantum Hall effect in 2D lattices. The first method is related to the topologically invariant Chern number of the system and I will emphasize the link between the quantized transverse conductivity and the edge states of the system. The second method is the Meir Wingreen formula. This really powerful formula is related to the green’s functions formalism. I will show the coherence of both methods.

Finally, I will study the effect of the disorder on quantum Hall systems and emphasize the existence of a disorder induced quantized conductance (topological Anderson insulator).

Date: 17 January 2012

Time: 14:30 h

Place: 3rd floor seminar lecture room. Dpto. Física Teórica. Facultad de Ciencias Físicas UCM

Experimental quantum computation with trapped ions

Philipp Schindler

Institute for Experimental Physics, University of Innsbruck

Nowadays it is widely known that a quantum computer can solve certain problems more efficient than any classical computer. In the group of Prof. Rainer Blatt in Innsbruck we try to realize such a quantum computer with the aid of trapped Ca+ ions. In the last year quantum state manipulation of a few trapped ions has evolved beyond the set of coherent universal quantum operations towards an efficient toolbox covering also dissipative processes. In this talk I will introduce our toolbox and talk about experiments in the field of quantum computation and quantum simulation. More specifically I will talk about the demonstration of repetitive quantum error correction [1] and the implementation of first steps towards a universal quantum simulator for open quantum systems [2].

[1] Experimental repetitive quantum error correction, P. Schindler et al, Science

332, 1059 (2011)

[2] An open-system quantum simulator with trapped ions, J. T. Barreiro, M. Müller et al, Nature 470, 486 (2011).

Date: 12 January 2012

Time: 13:30 h

Place: 3rd floor seminar lectura room. Dpto. Física Teórica I. Facultad de Ciencias Físicas, UCM

Shortcuts to adiabaticity in quantum devices

Adolfo del Campo

Los Álamos National Laboratory, Theoretical Division

“Fast good” is a new culinary concept envisioned by the chef F. Ad- rià aimed at creating a diet enjoying of two apparently mutually-ex- clusive features: fast-service and high-quality. When similar ideas are invoked in the quantum realm, one faces the adiabatic theorem which imposes a price. The preparation of a given target state with high-fidelity, free from spurious excitations, generally demands a long time of evolution and the implementation of an adiabatic dy- namics. In this talk, I will present recent theoretical advances and experimental progress in the design of shortcuts to adiabaticity in quantum systems by a variety of complementary approaches, such as the use of adiabatic invariants, inversion of dynamical scaling laws, the transitionless quantum driving algorithm, and inhomogen- eous quenches (time-permitting). These methods will be applied to the control of ultracold gases and trapped ions, with special em- phasis in many-body aspects. In particular, a proposal to realize a quantum dynamical microscope will be discussed.

Date: 20 Diciembre 2011

Time: 14:30 h

Place: 3rd floor seminar lecture room. Dpto. Física Teórica I. Facultad de Ciencias Físicas UCM

Entanglement renormalization, holography and correlations between disjoint regions in quantum critical systems

Javier Molina Vilaplana

Universidad Politécnica de Cartagena

Recently, it has been proposed that in (d+1) dimensional Multiscale Entanglement Renormalization  Ansatz  (MERA) networks,  tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdS) with the original system lying at the boundary. In thistalk we will provide additional support for this proposal by showing the explicit formal equivalence between the real space renormalization group (RG) flow of the two point correlators in different types of MERA states and the holographic RG flow of these correlators in asymptotically Anti de Sitter (AdS) spacetimes. Additionally, we analyze the MERA renormalization flow that arises when computing the correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdS black hole geometry when the mutual information (MI) between the blocks is computed using the Ryu- Takayanagi formula. As an explicit example, we use the BTZ AdS black hole to compute the MI between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value and discuss the robustness of this transition when finite size effects are taken into account.

Date: 15 de diciembre de 2011

Time: 14:30 h

Place: 3rd Floor seminar lecture room. Dpto. Física Teórica I. Facultad de Ciencias Físicas UCM