Density Matrix Renormalization Group for Dummies

We describe the Density Matrix Renormalization Group algorithms for time dependent and time independent Hamiltonians. This paper is a brief but comprehensive introduction to the subject for anyone willing to enter in the field or write the program source code from scratch.Comment: 29 pages, 9 figures. Published version. An open source version of the code can be found at http://qti.sns.it/dmrg/phome.htm

Entanglement production by quantum error correction in the presence of correlated environment

We analyze the effect of a quantum error correcting code on the entanglement of encoded logical qubits in the presence of a dephasing interaction with a correlated environment. Such correlated reservoir introduces entanglement between physical qubits. We show that for short times the quantum error correction interprets such entanglement as errors and suppresses it. However for longer time, although quantum error correction is no longer able to correct errors, it enhances the rate of entanglement production due to the interaction with the environment.Comment: 7 pages, 3 figures, published versio

Berry phase for a spin 1/2 in a classical fluctuating field

The effect of fluctuations in the classical control parameters on the Berry phase of a spin 1/2 interacting with a adiabatically cyclically varying magnetic field is analyzed. It is explicitly shown that in the adiabatic limit dephasing is due to fluctuations of the dynamical phase.Comment: 4 pages, 1 figure, published versio

Adiabatic quantum dynamics of a random Ising chain across its quantum critical point

We present here our study of the adiabatic quantum dynamics of a random Ising chain across its quantum critical point. The model investigated is an Ising chain in a transverse field with disorder present both in the exchange coupling and in the transverse field. The transverse field term is proportional to a function $\Gamma(t)$ which, as in the Kibble-Zurek mechanism, is linearly reduced to zero in time with a rate $\tau^{-1}$, $\Gamma(t)=-t/\tau$, starting at $t=-\infty$ from the quantum disordered phase ($\Gamma=\infty$) and ending at $t=0$ in the classical ferromagnetic phase ($\Gamma=0$). We first analyze the distribution of the gaps -- occurring at the critical point $\Gamma_c=1$ -- which are relevant for breaking the adiabaticity of the dynamics. We then present extensive numerical simulations for the residual energy $E_{\rm res}$ and density of defects $\rho_k$ at the end of the annealing, as a function of the annealing inverse rate $\tau$. %for different lenghts of the chain. Both the average $E_{\rm res}(\tau)$ and $\rho_k(\tau)$ are found to behave logarithmically for large $\tau$, but with different exponents, $[E_{\rm res}(\tau)/L]_{\rm av}\sim 1/\ln^{\zeta}(\tau)$ with $\zeta\approx 3.4$, and $[\rho_k(\tau)]_{\rm av}\sim 1/\ln^{2}(\tau)$. We propose a mechanism for $1/\ln^2{\tau}$-behavior of $[\rho_k]_{\rm av}$ based on the Landau-Zener tunneling theory and on a Fisher's type real-space renormalization group analysis of the relevant gaps. The model proposed shows therefore a paradigmatic example of how an adiabatic quantum computation can become very slow when disorder is at play, even in absence of any source of frustration.Comment: 10 pages, 11 figures; v2: added references, published versio

Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.Comment: 19 pages, 12 figure

Improved Core Genes Prediction for Constructing well-supported Phylogenetic Trees in large sets of Plant Species

The way to infer well-supported phylogenetic trees that precisely reflect the evolutionary process is a challenging task that completely depends on the way the related core genes have been found. In previous computational biology studies, many similarity based algorithms, mainly dependent on calculating sequence alignment matrices, have been proposed to find them. In these kinds of approaches, a significantly high similarity score between two coding sequences extracted from a given annotation tool means that one has the same genes. In a previous work article, we presented a quality test approach (QTA) that improves the core genes quality by combining two annotation tools (namely NCBI, a partially human-curated database, and DOGMA, an efficient annotation algorithm for chloroplasts). This method takes the advantages from both sequence similarity and gene features to guarantee that the core genome contains correct and well-clustered coding sequences (\emph{i.e.}, genes). We then show in this article how useful are such well-defined core genes for biomolecular phylogenetic reconstructions, by investigating various subsets of core genes at various family or genus levels, leading to subtrees with strong bootstraps that are finally merged in a well-supported supertree.Comment: 12 pages, 7 figures, IWBBIO 2015 (3rd International Work-Conference on Bioinformatics and Biomedical Engineering

Detection of gravitational waves from the QCD phase transition with pulsar timing arrays

If the cosmological QCD phase transition is strongly first order and lasts sufficiently long, it generates a background of gravitational waves which may be detected via pulsar timing experiments. We estimate the amplitude and the spectral shape of such a background and we discuss its detectability prospects.Comment: 7 pages, 5 figs. Version accepted by PR

Magnonic Charge Pumping via Spin-Orbit Coupling

The interplay between spin, charge, and orbital degrees of freedom has led to the development of spintronic devices like spin-torque oscillators, spin-logic devices, and spin-transfer torque magnetic random-access memories. In this development spin pumping, the process where pure spin-currents are generated from magnetisation precession, has proved to be a powerful method for probing spin physics and magnetisation dynamics. The effect originates from direct conversion of low energy quantised spin-waves in the magnet, known as magnons, into a flow of spins from the precessing magnet to adjacent normal metal leads. The spin-pumping phenomenon represents a convenient way to electrically detect magnetisation dynamics, however, precessing magnets have been limited so far to pump pure spin currents, which require a secondary spin-charge conversion element such as heavy metals with large spin Hall angle or multi-layer layouts to be detectable. Here, we report the experimental observation of charge pumping in which a precessing ferromagnet pumps a charge current, demonstrating direct conversion of magnons into high-frequency currents via the relativistic spin-orbit interaction. The generated electric current, differently from spin currents generated by spin-pumping, can be directly detected without the need of any additional spin to charge conversion mechanism and amplitude and phase information about the relativistic current-driven magnetisation dynamics. The charge-pumping phenomenon is generic and gives a deeper understanding of the recently observed spin-orbit torques, of which it is the reciprocal effect and which currently attract interest for their potential in manipulating magnetic information. Furthermore, charge pumping provides a novel link between magnetism and electricity and may find application in sourcing alternating electric currents.Comment: 3 figure

Concurrence in Disordered Systems

Quantum systems exist at finite temperatures and are likely to be disordered to some level. Since applications of quantum information often rely on entanglement, we require methods which allow entanglement measures to be calculated in the presence of disorder at non-zero temperatures. We demonstrate how the disorder averaged concurrence can be calculated using thermal many-body perturbation theory. Our technique can also be applied to other entanglement measures. To illustrate, we find the disorder averaged concurrence of an XX spin chain. We find that concurrence can be increased by disorder in some parameter regimes.Comment: 14 pages, 5 figure