Complexity in the presence of a boundary

The effects of a boundary on the circuit complexity are studied in two dimensional theories. The analysis is performed in the holographic realization of a conformal field theory with a boundary by employing different proposals for the dual of the complexity, including the \u201cComplexity = Volume\u201d (CV) and \u201cComplexity = Action\u201d (CA) prescriptions, and in the harmonic chain with Dirichlet boundary conditions. In all the cases considered except for CA, the boundary introduces a subleading logarithmic divergence in the expansion of the complexity as the UV cutoff vanishes. Holographic subregion complexity is also explored in the CV case, finding that it can change discontinuously under continuous variations of the configuration of the subregion

Entanglement of Two Disjoint Intervals in Conformal Field Theory and the 2D Coulomb Gas on a Lattice

In the conformal field theories given by the Ising and Dirac models, when the system is in the ground state, the moments of the reduced density matrix of two disjoint intervals and of its partial transpose have been written as partition functions on higher genus Riemann surfaces with symmetry. We show that these partition functions can be expressed as the grand canonical partition functions of the two-dimensional two component classical Coulomb gas on certain circular lattices at specific values of the coupling constant

Paleoclimatic and paleobiological correlations by mammal faunas from Southern America and SW Europe

Proceedings of the 1" R.C.A.N.S. Congress, Lisboa, October 1992The preliminary results of a research dealing with the study of global changes in the last 5 Ma by correlations of continental records between the Northern and the Southern Hemispheres (SW Europe and Argentina, respectively) are reported. The first analyses of the evolutionary patterns point out, in Argentina, two different turnover times: the first one is characterized by a high percentage of mammalautochthonous extinctions placed in the span of time between the last Chapadmalalan and the first Ensenadan faunas, around 2.5-2.3 Ma. It is possible to identify a high percentage of new immigrant genera from North America in the first turnover, while the second one, associated to the "last Pleistocene megafaunal extinctions", probably occurred at the beginning of the "Glacial Pleistocene", around 1.0-0.8 Ma. The oxygen isotope composition of phosphate from fossil mammal bones was measured to have a better climatic resolution from faunal elements of two hemispheres and to compare them by results as quantitative as possible. The preliminary efforts are brought out on fourteen deposits from SE Spain. Isotopic and chemical results strongly suggest the existence of a relation between the oxygen isotope composition in various skeletal components and the taphonomic processes of a single deposit. The variations of 0180 in the mammal teeth of Equidae from SE Spain suggest a shift towards a colder environment from the older one, Huelago, to more recent deposits, as well as from Venta Micena to Fuensanta in agreement with the transition from the Middle to the Upper Villafranchian, around 2.5 Ma, and the transition between the "Preglacial" to the "Glacial" Pleistocene, around 1.9-0.8 Ma

Liouville field theory with heavy charges. II. The conformal boundary case

We develop a general technique for computing functional integrals with fixed area and boundary length constraints. The correct quantum dimensions for the vertex functions are recovered by properly regularizing the Green function. Explicit computation is given for the one point function providing the first one loop check of the bootstrap formula.Comment: LaTeX 26 page

Occlusal traits in children with neurofibromatosis type 1

Literature is poor of data about the occlusion in children affected by neurofibromatosis type 1 (NF1). This case-control study investigated the occlusal traits in a group of children with NF1

Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories

This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability

Bose-Fermi duality and entanglement entropies

Entanglement (Renyi) entropies of spatial regions are a useful tool for characterizing the ground states of quantum field theories. In this paper we investigate the extent to which these are universal quantities for a given theory, and to which they distinguish different theories, by comparing the entanglement spectra of the massless Dirac fermion and the compact free boson in two dimensions. We show that the calculation of Renyi entropies via the replica trick for any orbifold theory includes a sum over orbifold twists on all cycles. In a modular-invariant theory of fermions, this amounts to a sum over spin structures. The result is that the Renyi entropies respect the standard Bose-Fermi duality. Next, we investigate the entanglement spectrum for the Dirac fermion without a sum over spin structures, and for the compact boson at the self-dual radius. These are not equivalent theories; nonetheless, we find that (1) their second Renyi entropies agree for any number of intervals, (2) their full entanglement spectra agree for two intervals, and (3) the spectrum generically disagrees otherwise. These results follow from the equality of the partition functions of the two theories on any Riemann surface with imaginary period matrix. We also exhibit a map between the operators of the theories that preserves scaling dimensions (but not spins), as well as OPEs and correlators of operators placed on the real line. All of these coincidences can be traced to the fact that the momentum lattice for the bosonized fermion is related to that of the self-dual boson by a 45 degree rotation that mixes left- and right-movers.Comment: 40 pages; v3: improvements to presentation, new section discussing entanglement negativit

Universal parity effects in the entanglement entropy of XX chains with open boundary conditions

We consider the Renyi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher-Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(1/l) for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary.Comment: 24 pages, 9 figure

Entanglement entropy of two disjoint intervals in conformal field theory

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any integer n is calculated as the four-point function of a particular type of twist fields and the final result is expressed in a compact form in terms of the Riemann-Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos corrected and refs adde