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

Localization in the Rindler Wedge

One of the striking features of QED is that charged particles create a coherent cloud of photons. The resultant coherent state vectors of photons generate a non-trivial representation of the localized algebra of observables that do not support a representation of the Lorentz group: Lorentz symmetry is spontaneously broken. We show in particular that Lorentz boost generators diverge in this representation, a result shown also in [1] (See also [2]). Localization of observables, for example in the Rindler wedge, uses Poincar\'e invariance in an essential way [3]. Hence in the presence of charged fields, the photon observables cannot be localized in the Rindler wedge. These observations may have a bearing on the black hole information loss paradox, as the physics in the exterior of the black hole has points of resemblance to that in the Rindler wedge.Comment: 11 page

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

Smoothly-varying hopping rates in driven flow with exclusion

We consider the one-dimensional totally asymmetric simple exclusion process (TASEP) with position-dependent hopping rates. The problem is solved,in a mean field/adiabatic approximation, for a general (smooth) form of spatial rate variation. Numerical simulations of systems with hopping rates varying linearly against position (constant rate gradient), for both periodic and open boundary conditions, provide detailed confirmation of theoretical predictions, concerning steady-state average density profiles and currents, as well as open-system phase boundaries, to excellent numerical accuracy.Comment: RevTeX 4.1, 14 pages, 9 figures (published version

Desidratação por imersão-impregnação e secagem por convecção de goiaba.

O objetivo deste trabalho foi avaliar as características físico-químicas e sensoriais de goiabas in natura e submetidas à desidratação por imersão-impregnação e à secagem complementar por convecção, além de avaliar a estabilidade da cor das goiabas secadas após 30, 60 e 90 dias de armazenamento sob refrigeração. Amostras de goiaba foram imersas em soluções de sacarose a 0,4 e 0,5 g mL-1, sacarose a 0,3 g mL-1 + sucralose a 0,2 g L-1, açúcar invertido a 41% (p/p) e açúcar invertido sem diluição. Foram avaliados sólidos solúveis totais, acidez titulável, pH, cor, aroma, aparência, sabor e textura. O teor de sólidos solúveis totais das amostras aumentou linearmente em função do tempo de imersão, sem efeito significativo do tipo de açúcar empregado no preparo da solução. A preservação do teor de ácido cítrico foi mais pronunciada em soluções menos concentradas de sacarose. Amostras secadas não submetidas à desidratação osmótica exibiram maior alteração de cor do que aquelas previamente desidratadas. Soluções de sacarose são mais eficazes na estabilidade da cor do que as de açúcar invertido. As goiabas submetidas à desidratação por imersão-impregnação tiveram boa aceitação sensorial, e aquelas secadas apenas por convecção não foram aceitas pelos provadores

Connectivity-dependent properties of diluted sytems in a transfer-matrix description

We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in non-zero matrix elements and allows one to use standard random-matrix multiplication techniques. Thus it is possible to investigate physical processes on the percolation structure with the high efficiency and precision characteristic of transfer-matrix methods, while avoiding disconnections. The method is illustrated for two-dimensional site percolation by calculating (i) the critical correlation length along the strip, and the finite-size longitudinal DC conductivity: (ii) at the percolation threshold, and (iii) very near the pure-system limit.Comment: 4 pages, no figures, RevTeX, Phys. Rev. E Rapid Communications (to be published

Functional Bosonization of Non-Relativistic Fermions in (2+1)(2+1) Dimensions

We analyze the universality of the bosonization rules in non-relativistic fermionic systems in $(2+1)d$. We show that, in the case of linear fermionic dispersion relations, a general fermionic theory can be mapped into a gauge theory in such a way that the fermionic density maps into a magnetic flux and the fermionic current maps into a transverse electric field. These are universal rules in the sense that they remain valid whatever the interaction considered. We also show that these rules are universal in the case of non-linear dispersion relations provided we consider only density-density interactions. We apply the functional bosonization formalism to a non-relativistic and non-local massive Thirring-like model and evaluate the spectrum of collective excitations in several limits. In the large mass limit, we are able to exactly calculate this spectrum for arbitrary density-density and current-current interactions. We also analyze the massless case and show that it has no collective excitations for any density-density potential in the Gaussian approximation. Moreover, the presence of current interactions may induce a gapless mode with a linear dispersion relation.Comment: 26 Pages, LaTeX, Final version to appear in International Journal of Modern Physics

Entanglement entropy in the Long-Range Kitaev chain

In this paper we complete the study on the asymptotic behaviour of the entanglement entropy for Kitaev chains with long range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for the asymptotic growth of the entropy appear. The coefficient of the leading term is not universal any more and the connection with conformal field theories is lost. We perform a numerical and analytical approach to the problem showing a perfect agreement. In order to carry out the analytical study, a new technique for computing the asymptotic behaviour of block Toeplitz determinants with discontinuous symbols has been developed.Comment: 20 pages, 5 figure