Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity ($F$) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of $F$ for an anisotropic quantum critical point for both thermodynamic and non-thermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of $F$ inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate $F$ through the overlap between the ground states for angle of rotation $\eta$ and $\eta+d\eta$, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.Comment: 10 pages, 8 figure

On the log correction to the black hole area law

Various approaches to black hole entropy yield the area law with logarithmic corrections, many involving a coefficient 1/2, and some involving 3/2. It is pointed out here that the standard quantum geometry formalism is not consistent with 3/2 and favours 1/2.Comment: 4 pages; added new result

Several Trade off Features of Quantum Steering in Distributed Scenario

In the present work, we address the question of how bipartite steering violation takes place among multi-partite systems (where each sub-system have Hilbert space dimension restricted to two) based on the maximal violations of the bipartite steering inequality of the reduced pairwise qubit systems. We have derived a trade-off relation which is satisfied by those pairwise bipartite maximal steering violations, which physically can be understood as providing restrictions on the distribution of steering among subsystems. For a three-qubit system, it is impossible that all pairs of qubits violate the steering inequality, and once a pair of qubits violates the steering inequality maximally, the other two pairs of qubits must both obey the steering inequality. We also present a complementarity relation between genuine entanglement present in a tripartite state and maximum bipartite steering violation by its reduced states.Comment: Close to published versio

The role of potential in the ghost-condensate dark energy model

We consider the ghost-condensate model of dark energy with a generic potential term. The inclusion of the potential is shown to give greater freedom in realising the phantom regime. The self-consistency of the analysis is demonstrated using WMAP7+BAO+Hubble data.Comment: A new sub-section added, 13 pages, 3 figures, LaTex. paper thoroughly rewritten. arXiv admin note: substantial text overlap with arXiv:1301.4746; and text overlap with arXiv:1008.2182 by other author