OTOC, complexity and entropy in bi-partite systems

There is a remarkable interest in the study of Out-of-time ordered correlators (OTOCs) that goes from many body theory and high energy physics to quantum chaos. In this latter case there is a special focus on the comparison with the traditional measures of quantum complexity such as the spectral statistics, for example. The exponential growth has been verified for many paradigmatic maps and systems. But less is known for multi-partite cases. On the other hand the recently introduced Wigner separability entropy (WSE) and its classical counterpart (CSE) provide with a complexity measure that treats equally quantum and classical distributions in phase space. We have compared the behavior of these measures in a system consisting of two coupled and perturbed cat maps with different dynamics: double hyperbolic (HH), double elliptic (EE) and mixed (HE). In all cases, we have found that the OTOCs and the WSE have essentially the same behavior, providing with a complete characterization in generic bi-partite systems and at the same time revealing them as very good measures of quantum complexity for phase space distributions. Moreover, we establish a relation between both quantities by means of a recently proven theorem linking the second Renyi entropy and OTOCs.Comment: 6 pages, 5 figure

Strong Coupling Theory for Interacting Lattice Models

We develop a strong coupling approach for a general lattice problem. We argue that this strong coupling perspective represents the natural framework for a generalization of the dynamical mean field theory (DMFT). The main result of this analysis is twofold: 1) It provides the tools for a unified treatment of any non-local contribution to the Hamiltonian. Within our scheme, non-local terms such as hopping terms, spin-spin interactions, or non-local Coulomb interactions are treated on equal footing. 2) By performing a detailed strong-coupling analysis of a generalized lattice problem, we establish the basis for possible clean and systematic extensions beyond DMFT. To this end, we study the problem using three different perspectives. First, we develop a generalized expansion around the atomic limit in terms of the coupling constants for the non-local contributions to the Hamiltonian. By analyzing the diagrammatics associated with this expansion, we establish the equations for a generalized dynamical mean-field theory (G-DMFT). Second, we formulate the theory in terms of a generalized strong coupling version of the Baym-Kadanoff functional. Third, following Pairault, Senechal, and Tremblay, we present our scheme in the language of a perturbation theory for canonical fermionic and bosonic fields and we establish the interpretation of various strong coupling quantities within a standard perturbative picture.Comment: Revised Version, 17 pages, 5 figure

Tolman mass, generalized surface gravity, and entropy bounds

In any static spacetime the quasi-local Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics and invoking the Unruh effect one can then develop elementary bounds on the quasi-local entropy that are very similar in spirit to the holographic bound, and closely related to entanglement entropy.Comment: V1: 4 pages. Uses revtex4-1; V2: Three references added; V3: Some notational changes for clarity; introductory paragraph rewritten; no physics changes. This version accepted for publication in Physical Review Letter

Understanding the Heavy Fermion Phenomenology from Microscopic Model

We solve the 3D periodic Anderson model via two impurity DMFT. We obtain the temperature v.s. hybridization phase diagram. In approaching the quantum critical point (QCP) both the Neel and lattice Kondo temperatures decrease and they do not cross at the lowest temperature we reached. While strong ferromagnetic spin fluctuation on the Kondo side is observed, our result indicates the critical static spin susceptibility is local in space at the QCP. We observe in the crossover region logarithmic temperature dependence in the specific heat coefficient and spin susceptibility

Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities

In this paper we establish an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and the triangulated category of singularities of the fiber of W over zero. The main result is a theorem that shows that the graded triangulated category of singularities of the cone over a projective variety is connected via a fully faithful functor to the bounded derived category of coherent sheaves on the base of the cone. This implies that the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W is connected via a fully faithful functor to the derived category of coherent sheaves on the projective variety defined by the equation W=0.Comment: 26 pp., LaTe

Vanadium dioxide : A Peierls-Mott insulator stable against disorder

Vanadium dioxide undergoes a first order metal-insulator transition at 340 K. In this work, we develop and carry out state of the art linear scaling DFT calculations refined with non-local dynamical mean-field theory. We identify a complex mechanism, a Peierls-assisted orbital selection Mott instability, which is responsible for the insulating M$_1$ phase, and furthermore survives a moderate degree of disorder.Comment: 5 pages, 4 figures. Supplementary material 8 pages, 4 figures. This version (v2) matches that accepted for Physical Review Letters on 16th May 201

A New Test of the Einstein Equivalence Principle and the Isotropy of Space

Recent research has established that nonsymmetric gravitation theories like Moffat's NGT predict that a gravitational field singles out an orthogonal pair of polarization states of light that propagate with different phase velocities. We show that a much wider class of nonmetric theories encompassed by the $\chi g$ formalism predict such violations of the Einstein equivalence principle. This gravity-induced birefringence of space implies that propagation through a gravitational field can alter the polarization of light. We use data from polarization measurements of extragalactic sources to constrain birefringence induced by the field of the Galaxy. Our new constraint is $10^8$ times sharper than previous ones.Comment: 21 pages, Latex, 3 Postscript figure

Scalar Field Oscillations Contributing to Dark Energy

We use action-angle variables to describe the basic physics of coherent scalar field oscillations in the expanding universe. These analytical mechanics methods have some advantages, like the identification of adiabatic invariants. As an application, we show some instances of potentials leading to equations of state with $p<-\rho/3$, thus contributing to the dark energy that causes the observed acceleration of the universe.Comment: 17 pages, 6 figures, Latex file. Sec.II reduced, discussion on sound speed added in Sec.IV, new references added. Accepted for publication in Physical Review

Multi-Partite Entanglement Inequalities via Spin Vector Geometry

We introduce inequalities for multi-partite entanglement, derived from the geometry of spin vectors. The criteria are constructed iteratively from cross and dot products between the spins of individual subsystems, each of which may have arbitrary dimension. For qubit ensembles the maximum violation for our inequalities is larger than that for the Mermin-Klyshko Bell inequalities, and the maximally violating states are different from Greenberger-Horne-Zeilinger states. Our inequalities are violated by certain bound entangled states for which no Bell-type violation has yet been found.Comment: 4 pages, 2 tables, 1 figure. A truncated version is published in Physical Review Letters, volume 95 issue 18, 180402 (October 2005