Entanglement between collective operators in a linear harmonic chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several noncontiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.

Time-dependent tight binding

Starting from a Lagrangian mean-field theory, a set of time-dependent tight-binding equations is derived to describe dynamically and self-consistently an interacting system of quantum electrons and classical nuclei. These equations conserve norm, total energy and total momentum. A comparison with other tight-binding models is made. A previous tight-binding result for forces on atoms in the presence of electrical current flow is generalized to the time-dependent domain and is taken beyond the limit of local charge neutrality.

Entanglement entropy dynamics of Heisenberg chains

By means of the time dependent density matrix renormalization group algorithm we study the zero-temperature dynamics of the Von Neumann entropy of a block of spins in a Heisenberg chain after a sudden quench in the anisotropy parameter. In the absence of any disorder the block entropy increases linearly with time and then saturates. We analyse the velocity of propagation of the entanglement as a function of the initial and final anisotropies and compare our results, wherever possible, with those obtained by means of conformal field theory. In the disordered case we find a slower ( logarithmic) evolution which may signal the onset of entanglement localization.

Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix ?1, ?2, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.

Entanglement properties of spin models in triangular lattices

The different quantum phases appearing in strongly correlated systems as well as their transitions are closely related to the entanglement shared between their constituents. In 1D systems, it is well established that the entanglement spectrum is linked to the symmetries that protect the different quantum phases. This relation extends even further at the phase transitions where a direct link associates the entanglement spectrum to the conformal field theory describing the former. For 2D systems much less is known. The lattice geometry becomes a crucial aspect to consider when studying entanglement and phase transitions. Here, we analyze the entanglement properties of triangular spin lattice models by also considering concepts borrowed from quantum information theory such as geometric entanglement.

Dielectrics in a time-dependent electric field: a real-time approach based on density-polarization functional theory

In the presence of a (time-dependent) macroscopic electric field the electron dynamics of dielectrics cannot be described by the time-dependent density only. We present a real-time formalism that has the density and the macroscopic polarization P as key quantities. We show that a simple local function of P already captures long-range correlation in linear and nonlinear optical response functions. Specifically, after detailing the numerical implementation, we examine the optical absorption, the second- and third-harmonic generation of bulk Si, GaAs, AlAs and CdTe at different level of approximation. We highlight links with ultranonlocal exchange-correlation functional approximations proposed within linear response time-dependent density functional theory framework.

A New Theory for Perpendicular Transport of Cosmic Rays

We present an improved nonlinear theory for the perpendicular transport of charged particles. This approach is based on an improved nonlinear treatment of field-line random walk in combination with a generalized compound diffusion model. The generalized compound diffusion model employed is more systematic and reliable, in comparison with previous theories. Furthermore, the theory shows remarkably good agreement with test-particle simulations and solar wind observations.

Analytical description of stochastic field-Line wandering in magnetic turbulence

A nonperturbative nonlinear statistical approach is presented to describe turbulent magnetic systems embedded in a uniform mean magnetic field. A general formula in the form of an ordinary differential equation for magnetic field-line wandering (random walk) is derived. By considering the solution of this equation for different limits several new results are obtained. As an example, it is demonstrated that the stochastic wandering of magnetic field-lines in a two-component turbulence model leads to superdiffusive transport, contrary to an existing diffusive picture. The validity of quasilinear theory for field-line wandering is discussed, with respect to different turbulence geometry models, and previous diffusive results are shown to be deduced in appropriate limits.

Recent advances in understanding CO oxidation on gold nanoparticles using density functional theory

Since the discovery of a series of Au-based catalysts by Haruta et al. considerable progress has been made in understanding the active role of Au in CO oxidation catalysis. This review provides a summary of recent theoretical work performed in this field; in particular it addresses DFT studies of CO oxidation catalysis over free and supported gold nanoparticles. Several properties of the Au particles have been found to contribute to their unique catalytic activity. Of these properties, the low-coordination state of the Au atoms is arguably the most pertinent, although other properties of the Au cluster atoms, such as electronic charge, cannot be ignored. The current consensuses regarding the mechanism for CO oxidation over Au-based catalysts is also discussed. Finally, water-enhanced catalysis of CO oxidation on Au clusters is summarized.

Identifying an O-2 supply pathway in CO oxidation on Au/TiO2(110): A density functional theory study on the intrinsic role of water

Au catalysis has been one of the hottest topics in chemistry in the last 10 years or so. How O-2 is supplied and what role water plays in CO oxidation are the two challenging issues in the field at the moment. In this study, using density functional theory we show that these two issues are in fact related to each other. The following observations are revealed: (i) water that can dissociate readily into OH groups can facilitate O-2 adsorption on TiO2; (ii) the effect of OH group on the O-2 adsorption is surprisingly long-ranged; and (iii) O-2 can also diffuse along the channel of Ti (5c) atoms on TiO2(1 10), and this may well be the rate-limiting step for the CO oxidation. We provide direct evidence that O-2 is supplied by O-2 adsorption on TiO2 in the presence of OH and can diffuse to the interface of Au/TiO2 to participate in CO oxidation. Furthermore, the physical origin of the water effects on Au catalysis has been identified by electronic structure analyses: There is a charge transfer from TiO2 in the presence of OH to O-2, and the O-2 adsorption energy depends linearly on the 02 charge. These results are of importance to understand water effects in general in heterogeneous catalysis.

Catalytic role of gold in gold-based catalysts: A density functional theory study on the CO oxidation on gold

Gold-based catalysts have been of intense interests in recent years, being regarded as a new generation of catalysts due to their unusually high catalytic performance. For example, CO oxidation on Au/TiO2 has been found to occur at a temperature as low as 200 K. Despite extensive studies in the field, the microscopic mechanism of CO oxidation on Au-based catalysts remains controversial. Aiming to provide insight into the catalytic roles of Au, we have performed extensive density functional theory calculations for the elementary steps in CO oxidation on Au surfaces. O atom adsorption, CO adsorption, O-2 dissociation, and CO oxidation on a series of Au surfaces, including flat surfaces, defects and small clusters, have been investigated in detail. Many transition states involved are located, and the lowest energy pathways are determined. We find the following: (i) the most stable site for O atom on Au is the bridge site of step edge, not a kink site; (ii) O-2 dissociation on Au (O-2-->20(ad)) is hindered by high barriers with the lowest barrier being 0.93 eV on a step edge; (iii) CO can react with atomic O with a substantially lower barrier, 0.25 eV, on Au steps where CO can adsorb; (iv) CO can react with molecular O-2 on Au steps with a low barrier of 0.46 eV, which features an unsymmetrical four-center intermediate state (O-O-CO); and (v) O-2 can adsorb on the interface of Au/TiO2 with a reasonable chemisorption energy. On the basis of our calculations, we suggest that (i) O-2 dissociation on Au surfaces including particles cannot occur at low temperatures; (ii) CO oxidation on Au/inactive-materials occurs on Au steps via a two-step mechanism: CO+O-2-->CO2+O, and CO+O-->CO2; and (iii) CO oxidation on Au/active-materials also follows the two-step mechanism with reactions occurring at the interface.