Geometry versus Entanglement in Resonating Valence Bond Liquids

We investigate the behavior of bipartite as well as genuine multipartite entanglement of a resonating valence bond state on a ladder. We show that the system possesses significant amounts of bipartite entanglement in the steps of the ladder while no substantial bipartite entanglement is present in the rails. Genuine multipartite entanglement present in the system is negligible. The results are in stark contrast with the entanglement properties of the same state on isotropic lattices in two and higher dimensions, indicating that the geometry of the lattice can have important implications on the quality of quantum information and other tasks that can be performed by using multiparty states on that lattice.Comment: 6 pages, 8 figures, RevTeX

Fundamental Strings in Open String Theory at the Tachyonic Vacuum

We show that the world-volume theory on a D-p-brane at the tachyonic vacuum has solitonic string solutions whose dynamics is governed by the Nambu-Goto action of a string moving in (25+1) dimensional space-time. This provides strong evidence for the conjecture that at this vacuum the full (25+1) dimensional Poincare invariance is restored. We also use this result to argue that the open string field theory at the tachyonic vacuum must contain closed string excitations.Comment: LaTeX file, 16 pages, references and clarification adde

Density Matrix Recursion Method: Genuine Multisite Entanglement Distinguishes Odd from Even Quantum Heisenberg Ladders

We introduce an analytical iterative method, the density matrix recursion method, to generate arbitrary reduced density matrices of superpositions of short-range dimer coverings on periodic or non-periodic quantum spin-1/2 ladder lattices, with an arbitrary number of legs. The method can be used to calculate bipartite as well as multipartite physical properties, including bipartite and multi-partite entanglement. We apply this technique to distinguish between even- and odd-legged ladders. Specifically, we show that while genuine multi-partite entanglement decreases with increasing system size for the even-legged ladder states, it does the opposite for odd-legged ones.Comment: 13 pages, 3 figures, iopart.cls, final edited versio

The Mass, Normalization and Late Time behavior of the Tachyon Field

We study the dynamics of the tachyon field $T$. We derive the mass of the tachyon as the pole of the propagator which does not coincide with the standard mass given in the literature in terms of the second derivative of $V(T)$ or $Log[V(T)]$. We determine the transformation of the tachyon in order to have a canonical scalar field $\phi$. This transformation reduces to the one obtained for small $\dot T$ but it is also valid for large values of $\dot T$. This is specially interesting for the study of dark energy where $\dot T\simeq 1$. We also show that the normalized tachyon field $\phi$ is constrained to the interval $T_2\leq T \leq T_1$ where $T_1,T_2$ are zeros of the original potential $V(T)$. This results shows that the field $\phi$ does not know of the unboundedness of $V(T)$, as suggested for bosonic open string tachyons. Finally we study the late time behavior of tachyon field using the L'H\^{o}pital rule.Comment: 9 pages, 10 figure

Statistics of leading digits leads to unification of quantum correlations

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the information-theoretic paradigm, exhibit a universal behaviour. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distribution corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as the Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information theoretic measures violate the Benford's law. We quantitatively discuss the violation of the Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions.Comment: v1: 11 pages, 5 figures, 2 tables; v2: 11 pages, 6 figures, 2 tables, new results added, extended version of the published pape

Decay of Unstable D-branes with Electric Field

Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly evaluate the time dependence of the energy momentum tensor and the fundamental string charge density associated with this solution. The final decay product can be interpreted as a combination of stretched fundamental strings and tachyon matter.Comment: 35 pages, LaTe