Page Curves for General Interacting Systems

We calculate in detail the Renyi entanglement entropies of cTPQ states as a function of subsystem volume, filling the details of our prior work [Nature Communications 9, 1635 (2018)], where the formulas were first presented. Working in a limit of large total volume, we find universal formulas for the Renyi entanglement entropies in a region where the subsystem volume is comparable to that of the total system. The formulas are applicable to the infinite temperature limit as well as general interacting systems. For example we find that the second Renyi entropy of cTPQ states in terms of subsystem volume is written universally up to two constants, $S_2(\ell)=-\ln K(\beta)+\ell\ln a(\beta)-\ln\left(1+a(\beta)^{-L+2\ell}\right)$, where $L$ is the total volume of the system and $a$ and $K$ are two undetermined constants. The uses of the formulas were already presented in our prior work and we mostly concentrate on the theoretical aspect of the formulas themselves. Aside from deriving the formulas for the Renyi Page curves, the expression for the von Neumann Page curve is also derived, which was not presented in our previous work.Comment: 29 pages, 3 figures; JHEP preparatio

Fourth-order gravity as the inflationary model revisited

We revisit the old (fourth-order or quadratically generated) gravity model of Starobinsky in four space-time dimensions, and derive the (inflaton) scalar potential in the equivalent scalar-tensor gravity model via a Legendre-Weyl transform. The inflaton scalar potential is used to compute the (CMB) observables of inflation associated with curvature perturbations (namely, the scalar and tensor spectral indices, and the tensor-to-scalar ratio), including the new next-to-leading-order terms with respect to the inverse number of e-foldings. The results are compared to the recent (WMAP5) experimental bounds. We confirm both mathematical and physical equivalence between f(R) gravity theories and the corresponding scalar-tensor gravity theories.Comment: 10 pages, 1 figure, 1 table, LaTeX; few comments added, style improved, references added and update

Letter from Tow-o-goh-le, Waw-che-waw-he, and Sho-me-casse-tunga to George Sibley, April 5, 1810

Transcript of Letter from Tow-o-goh-le, Waw-che-waw-he, and Sho-me-casse-tunga to George Sibley, April 5, 1810. Chiefs acknowledge that members of their tribes have been robbing people and will compensate

Adventures in Holographic Dimer Models

We abstract the essential features of holographic dimer models, and develop several new applications of these models. First, semi-holographically coupling free band fermions to holographic dimers, we uncover novel phase transitions between conventional Fermi liquids and non-Fermi liquids, accompanied by a change in the structure of the Fermi surface. Second, we make dimer vibrations propagate through the whole crystal by way of double trace deformations, obtaining nontrivial band structure. In a simple toy model, the topology of the band structure experiences an interesting reorganization as we vary the strength of the double trace deformations. Finally, we develop tools that would allow one to build, in a bottom-up fashion, a holographic avatar of the Hubbard model.Comment: 22 pages, 8 figures; v2: brief description of case of pure D5 lattice added in sec.3; v3: minor typo fixed; v4: minor change