Dimerized ground states in spin-S frustrated systems

We study a family of frustrated anti-ferromagnetic spin-$S$ systems with a fully dimerized ground state. This state can be exactly obtained without the need to include any additional three-body interaction in the model. The simplest members of the family can be used as a building block to generate more complex geometries like spin tubes with a fully dimerized ground state. After present some numerical results about the phase diagram of these systems, we show that the ground state is robust against the inclusion of weak disorder in the couplings as well as several kinds of perturbations, allowing to study some other interesting models as a perturbative expansion of the exact one. A discussion on how to determine the dimerization region in terms of quantum information estimators is also presented. Finally, we explore the relation of these results with a the case of the a 4-leg spin tube which recently was proposed as the model for the description of the compound Cu$_2$Cl$_4$D$_8$C$_4$SO$_2$, delimiting the region of the parameter space where this model presents dimerization in its ground state.Comment: 10 pages, 9 figure

Phase diagram study of a dimerized spin-S zig-zag ladder

The phase diagram of a frustrated spin-$S$ zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary $S$, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground state, being the Majumdar-Ghosh point a particular member of the family. We show that the system presents a transition between a dimerized phase to a N\'eel-like phase for $S=1/2$, and spiral phases can appear for large $S$. The phase diagram is characterized by means of a generalization of the usual Mean Field Approximation (MFA). The novelty in the present implementation is to consider the strongest coupled sites as the unit cell. The gap and the excitation spectrum is analyzed through the Random Phase Approximation (RPA). Also, a perturbative treatment to obtain the critical points is discussed. Comparisons of the results with numerical methods like DMRG are also presented.Comment: 14 pages, 6 figures. Some typos were corrected, and notation was clarifie

Measurements, quantum discord and parity in spin 1 systems

We consider the evaluation of the quantum discord and other related measures of quantum correlations in a system formed by a spin 1 and a complementary spin system. A characterization of general projective measurements in such system in terms of spin averages is thereby introduced, which allows to easily visualize their deviation from standard spin measurements. It is shown that the measurement optimizing these measures corresponds in general to a non-spin measurement. The important case of states that commute with the total $S_z$ spin parity is discussed in detail, and the general stationary measurements for such states (parity preserving measurements) are identified. Numerical and analytical results for the quantum discord, the geometric discord and the one way information deficit in the relevant case of a mixture of two aligned spin 1 states are also presented.Comment: 6 pages, 2 figures, References adde

kmos: A lattice kinetic Monte Carlo framework

Kinetic Monte Carlo (kMC) simulations have emerged as a key tool for microkinetic modeling in heterogeneous catalysis and other materials applications. Systems, where site-specificity of all elementary reactions allows a mapping onto a lattice of discrete active sites, can be addressed within the particularly efficient lattice kMC approach. To this end we describe the versatile kmos software package, which offers a most user-friendly implementation, execution, and evaluation of lattice kMC models of arbitrary complexity in one- to three-dimensional lattice systems, involving multiple active sites in periodic or aperiodic arrangements, as well as site-resolved pairwise and higher-order lateral interactions. Conceptually, kmos achieves a maximum runtime performance which is essentially independent of lattice size by generating code for the efficiency-determining local update of available events that is optimized for a defined kMC model. For this model definition and the control of all runtime and evaluation aspects kmos offers a high-level application programming interface. Usage proceeds interactively, via scripts, or a graphical user interface, which visualizes the model geometry, the lattice occupations and rates of selected elementary reactions, while allowing on-the-fly changes of simulation parameters. We demonstrate the performance and scaling of kmos with the application to kMC models for surface catalytic processes, where for given operation conditions (temperature and partial pressures of all reactants) central simulation outcomes are catalytic activity and selectivities, surface composition, and mechanistic insight into the occurrence of individual elementary processes in the reaction network.Comment: 21 pages, 12 figure

Coherent control of quantum systems as a resource theory

Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a technological point of view. In this work, we establish a resource theory describing this setting and explore relations to the theory of coherence, entanglement and information processing. Specifically, for the coherent control of quantum systems the relevant resources of entanglement and coherence are found to be equivalent and closely related to a measure of discord. The results are then applied to the DQC1 protocol and the precision of the final measurement is expressed in terms of the available resources.Comment: 9 pages, 4 figures, final version. Discussions were improved and some points were clarified. The title was slightly changed to agree with the published versio

Factorization and entanglement in general XYZ spin arrays in non-uniform transverse fields

We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through $XYZ$ couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the $XXZ$ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the $j^{\rm th}$ spin in an open spin $s$ chain for different values of $s$ and $j$ are as well provided.Comment: 6 pages, figures adde

Generalized mean field description of entanglement in dimerized spin systems

We discuss a generalized self-consistent mean field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin 1/2 systems with anisotropic ferromagnetic-type XY and XYZ couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single spin MF. Its phase diagram differs significantly from that of the latter, exhibiting (Sz) parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration, the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.Comment: 13 pages, 9 figures. Final versio

The intrinsic complexity of parametric elimination methods

This paper is devoted to the complexity analysis of a particular property, called "algebraic robustness" owned by all known symbolic methods of parametric polynomial equation solving (geometric elimination). It is shown that any parametric elimination procedure which owns this property must neccessarily have an exponential sequential time complexity.Comment: LaTeX, 12 pages. To appear in Proc. of WAIT'97, Buenos Aires, Argentina, 199

Thermal entanglement in fully connected spin systems and its RPA description

We examine the thermal pairwise entanglement in a symmetric system of $n$ spins fully connected through anisotropic $XYZ$-type couplings embedded in a transverse magnetic field. We consider both the exact evaluation together with that obtained with the static path + random phase approximation (RPA) and the ensuing mean field + RPA. The latter is shown to provide an accurate analytic description of both the parallel and antiparallel thermal concurrence in large systems. We also analyze the limit temperature for pairwise entanglement, which is shown to increase for large fields and to decrease logarithmically with increasing $n$. Special finite size effects are as well discussed.Comment: 9 pages, 5 figure