Quantum Entanglement of Fermionic Local Operators

In this paper we study the time evolution of (Renyi) entanglement entropies for locally excited states in four dimensional free massless fermionic field theory. Locally excited states are defined by being acted by various local operators on the ground state. Their excesses are defined by subtracting (Renyi) entanglement entropy for the ground state from those for locally excited states. They finally approach some constant if the subsystem is given by half of the total space. They have spin dependence. They can be interpreted in terms of quasi-particles.Comment: 29pages, 7 figure

Edge theory approach to topological entanglement entropy, mutual information and entanglement negativity in Chern-Simons theories

We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus $g$, which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the $R$-symbols, monodromy and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent non-contractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.Comment: 30 pages, 8 figures; Reference and discussions on double torus are adde

Momentum space metric, non-local operator, and topological insulators

Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In particular, we introduce a non-local operator which represents distance square in real space and show that this corresponds to the Laplacian in curved momentum space, and also derive its path integral representation in momentum space. The quantum metric itself measures the second cumulant of the position operator in real space, much like the Berry gauge potential measures the first cumulant or the electric polarization in real space. By using the non-local operator and the metric, we study some aspects of topological phases such as topological invariants, the cumulants and topological phase transitions. The effect of interactions to the momentum space geometry is also discussed.Comment: 13 pages, 4 figure

Affleck-Dine Baryogenesis and heavy elements production from Inhomogeneous Big Bang Nucleosynthesis

We study the impact of possible high density baryonic bubbles on the early formed QSO, IGM, and metal poor stars. Such bubbles could be created, under certain conditions, in Affleck-Dine model of baryogenesis and may occupy a relatively small fraction of space, while the dominant part of the cosmological volume has the normal observed baryon-to-photon ratio $\eta = 6\cdot 10^{-10}$. The value of $\eta$ in the bubbles, could be much larger than the usually accepted one (it might be even close to unity) without contradicting the existing data on light element abundances and the observed angular spectrum of CMBR. We find upper bounds on $\eta$ by comparing heavy elements' abundances produced in BBN and those of metal poor stars. We conclude that $\eta$ should be smaller than $10^{-5}$ in some metal poor star regions.Comment: 11 pages, 4 figures, PTPTeX ; added references, changed introduction, acknowledgments and figure

Probing N=4 SYM With Surface Operators

In this paper we study surface operators in N=4 supersymmetric Yang-Mills theory. We compute surface operator observables, such as the expectation value of surface operators, the correlation function of surface operators with local operators, and the correlation function of surface operators with Wilson and 't Hooft loops. The calculations are performed using three different realizations of surface operators, corresponding respectively to the gauge theory path integral definition, the probe brane description in AdS_5xS^5 and the "bubbling'' supergravity description of surface operators. We find remarkable agreement between the different calculations performed using the three different realizations.Comment: 65 pages; lanlmac, 2 figure