Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte

DEFENSE BUDGET FLEXIBILITY AND CONTROL: HOW THE U.S. AND BRAZILIAN SYSTEMS STRIKE A BALANCE BETWEEN THE TWO

A recurrent challenge affecting defense budgeting systems across federalist nations is balancing budget flexibility and legislative control of military appropriations execution. There has been considerable debate over the unique nature of defense expenditure and how it reflects fiscal considerations. While budget revisions are necessary to maintain flexibility due to the broad scope of the defense budget and the handling of unforeseen events, adherence to financial goals and accountability for what was allowed by the legislative impose control over military expenditures, restricting the military's versatility in carrying out its appropriations. This project offers why balancing flexibility and control is crucial for both parties to achieve their objectives during the budget execution stage. Then, it determines the attributes that indicate an effective control system and adequate budget flexibility. Finally, it contrasts flexibility tools and control activities between the United States and Brazil. This project analyzes constitutional or other legal authority disparities between the legislature, chief executive, military, treasury, and other actors involved in budgeting systems and defense budget implementation to accomplish these goals. The Congressional Budget Office (CBO), Congressional Research Service (CRS), Office of Management and Budget (OMB), the National Treasury of Brazil (STN), the Federal Budget Secretary (SOF), and other reports are reviewed.Capitao-Tenente, Brazilian NavyApproved for public release. Distribution is unlimited

The CTA aims at the Inert Doublet Model

We show that the Cherenkov Telescope Array (CTA) can realistically challenge the Inert Doublet Model, excluding its heavy regime up to dark matter masses of 800 GeV and probing a large fraction of the remaining viable parameter space at even higher masses. Two features of the Inert Doublet Model make it particularly suitable for CTA searches. First, the dark matter mass (in the heavy regime) must be larger than 500 GeV. Second, the dark matter annihilation cross section, $\sigma v$, is always larger than the thermal one, reaching values as high as $10^{-25} \mathrm{cm^3s^{-1}}$. This higher value of $\sigma v$ is the result of the unavoidable coannhilation effects that determine the relic density via thermal freeze-out in the early Universe. We find that with 100 hours of Galactic Center exposure, CTA's expected limit widely surpasses, even after the inclusion of systematic errors, current and projected bounds from Fermi-LAT and HESS on this model