Increasing entanglement through engineered disorder in the random Ising chain

The ground state entanglement entropy between block of sites in the random Ising chain is studied by means of the Von Neumann entropy. We show that in presence of strong correlations between the disordered couplings and local magnetic fields the entanglement increases and becomes larger than in the ordered case. The different behavior with respect to the uncorrelated disordered model is due to the drastic change of the ground state properties. The same result holds also for the random 3-state quantum Potts model.Comment: 4 pages, published version, a few typos correcte

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 detection in hybrid optomechanical systems

We study a device formed by a Bose Einstein condensate (BEC) coupled to the field of a cavity with a moving end-mirror and find a working point such that the mirror-light entanglement is reproduced by the BEC-light quantum correlations. This provides an experimentally viable tool for inferring mirror-light entanglement with only a limited set of assumptions. We prove the existence of tripartite entanglement in the hybrid device, persisting up to temperatures of a few milli-Kelvin, and discuss a scheme to detect it.Comment: 6 pages, 7 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

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

Schmidt gap in random spin chains

We numerically investigate the low-lying entanglement spectrum of the ground state of random one-dimensional spin chains obtained after partition of the chain into two equal halves. We consider two paradigmatic models: the spin-1/2 random transverse field Ising model, solved exactly, and the spin-1 random Heisenberg model, simulated using the density matrix renormalization group. In both cases we analyze the mean Schmidt gap, defined as the difference between the two largest eigenvalues of the reduced density matrix of one of the two partitions, averaged over many disorder realizations. We find that the Schmidt gap detects the critical point very well and scales with universal critical exponents.Comment: Published version. 7 pages, 6 figure

Early clinical predictors and correlates of long-term morbidity in bipolar disorder

OBJECTIVES: Identifying factors predictive of long-term morbidity should improve clinical planning limiting disability and mortality associated with bipolar disorder (BD). METHODS: We analyzed factors associated with total, depressive and mania-related long-term morbidity and their ratio D/M, as %-time ill between a first-lifetime major affective episode and last follow-up of 207 BD subjects. Bivariate comparisons were followed by multivariable linear regression modeling. RESULTS: Total % of months ill during follow-up was greater in 96 BD-II (40.2%) than 111 BD-I subjects (28.4%; P=0.001). Time in depression averaged 26.1% in BD-II and 14.3% in BD-I, whereas mania-related morbidity was similar in both, averaging 13.9%. Their ratio D/M was 3.7-fold greater in BD-II than BD-I (5.74 vs. 1.96; P<0.0001). Predictive factors independently associated with total %-time ill were: [a] BD-II diagnosis, [b] longer prodrome from antecedents to first affective episode, and [c] any psychiatric comorbidity. Associated with %-time depressed were: [a] BD-II diagnosis, [b] any antecedent psychiatric syndrome, [c] psychiatric comorbidity, and [d] agitated/psychotic depressive first affective episode. Associated with %-time in mania-like illness were: [a] fewer years ill and [b] (hypo)manic first affective episode. The long-term D/M morbidity ratio was associated with: [a] anxious temperament, [b] depressive first episode, and [c] BD-II diagnosis. CONCLUSIONS: Long-term depressive greatly exceeded mania-like morbidity in BD patients. BD-II subjects spent 42% more time ill overall, with a 3.7-times greater D/M morbidity ratio, than BD-I. More time depressed was predicted by agitated/psychotic initial depressive episodes, psychiatric comorbidity, and BD-II diagnosis. Longer prodrome and any antecedent psychiatric syndrome were respectively associated with total and depressive morbidity

Complex phenotype in an Italian family with a novel mutation in SPG3A.

Mutations in the SPG3A gene represent a significant cause of autosomal dominant hereditary spastic paraplegia with early onset and pure phenotype. We describe an Italian family manifesting a complex phenotype, characterized by cerebellar involvement in the proband and amyotrophic lateral sclerosis-like syndrome in her father, in association with a new mutation in SPG3A. Our findings further widen the notion of clinical heterogeneity in SPG3A mutations

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