Bi-partite Entanglement Entropy in Massive QFT with a Boundary: the Ising Model

In this paper we give an exact infinite-series expression for the bi-partite entanglement entropy of the quantum Ising model in the ordered regime, both with a boundary magnetic field and in infinite volume. This generalizes and extends previous results involving the present authors for the bi-partite entanglement entropy of integrable quantum field theories, which exploited the generalization of the form factor program to branch-point twist fields. In the boundary case, we isolate in a universal way the part of the entanglement entropy which is related to the boundary entropy introduced by Affleck and Ludwig, and explain how this relation should hold in more general QFT models. We provide several consistency checks for the validity of our form factor results, notably, the identification of the leading ultraviolet behaviour both of the entanglement entropy and of the two-point function of twist fields in the bulk theory, to a great degree of precision by including up to 500 form factor contributions

Ising Field Theory on a Pseudosphere

We show how the symmetries of the Ising field theory on a pseudosphere can be exploited to derive the form factors of the spin fields as well as the non-linear differential equations satisfied by the corresponding two-point correlation functions. The latter are studied in detail and, in particular, we present a solution to the so-called connection problem relating two of the singular points of the associated Painleve VI equation. A brief discussion of the thermodynamic properties is also presented.Comment: 39 pages, 6 eps figures, uses harvma

On Painleve VI transcendents related to the Dirac operator on the hyperbolic disk

Dirac hamiltonian on the Poincare disk in the presence of an Aharonov-Bohm flux and a uniform magnetic field admits a one-parameter family of self-adjoint extensions. We determine the spectrum and calculate the resolvent for each element of this family. Explicit expressions for Green functions are then used to find Fredholm determinant representations for the tau function of the Dirac operator with two branch points on the Poincare disk. Isomonodromic deformation theory for the Dirac equation relates this tau function to a one-parameter class of solutions of the Painleve VI equation with $\gamma=0$. We analyze long distance behaviour of the tau function, as well as the asymptotics of the corresponding Painleve VI transcendents as $s\to 1$. Considering the limit of flat space, we also obtain a class of solutions of the Painleve V equation with $\beta=0$.Comment: 38 pages, 5 figure

More General Correlation Functions of Twist Fields From Ward Identities in the Massive Dirac Theory

Following on from previous work we derive the non-linear differential equations of more general correlators of U(1) twist fields in two-dimensional massive Dirac theory. Using the conserved charges of the double copy model equations parametrising the correlators of twist fields with arbitrary twist parameter are found. This method also gives a parametrisation of the correlation functions of general, fermionic, descendent twist fields. The equations parametrising correlators of primary twist fields are compared to those of the literature and evidence is presented to confirm that these equations represent the correct parametrisation.Comment: 18 pages, 1 figur

Form factors of twist fields in the lattice Dirac theory

We study U(1) twist fields in a two-dimensional lattice theory of massive Dirac fermions. Factorized formulas for finite-lattice form factors of these fields are derived using elliptic parametrization of the spectral curve of the model, elliptic determinant identities and theta functional interpolation. We also investigate the thermodynamic and the infinite-volume scaling limit, where the corresponding expressions reduce to form factors of the exponential fields of the sine-Gordon model at the free-fermion point.Comment: 20 pages, 2 figure

Angular Differential Imaging: a Powerful High-Contrast Imaging Technique

Angular differential imaging is a high-contrast imaging technique that reduces quasi-static speckle noise and facilitates the detection of nearby companions. A sequence of images is acquired with an altitude/azimuth telescope while the instrument field derotator is switched off. This keeps the instrument and telescope optics aligned and allows the field of view to rotate with respect to the instrument. For each image, a reference PSF is constructed from other appropriately-selected images of the same sequence and subtracted to remove quasi-static PSF structure. All residual images are then rotated to align the field and are combined. Observed performances are reported for Gemini North data. It is shown that quasi-static PSF noise can be reduced by a factor \~5 for each image subtraction. The combination of all residuals then provides an additional gain of the order of the square root of the total number of acquired images. A total speckle noise attenuation of 20-50 is obtained for one-hour long observing sequences compared to a single 30s exposure. A PSF noise attenuation of 100 was achieved for two-hour long sequences of images of Vega, reaching a 5-sigma contrast of 20 magnitudes for separations greater than 8". For a 30-minute long sequence, ADI achieves 30 times better signal-to-noise than a classical observation technique. The ADI technique can be used with currently available instruments to search for ~1MJup exoplanets with orbits of radii between 50 and 300 AU around nearby young stars. The possibility of combining the technique with other high-contrast imaging methods is briefly discussed.Comment: 27 pages, 7 figures, accepted for publication in Ap

Entanglement Content of Quantum Particle Excitations II. Disconnected Regions and Logarithmic Negativity

In this paper we study the increment of the entanglement entropy and of the (replica) logarithmic negativity in a zero-density excited state of a free massive bosonic theory, compared to the ground state. This extends the work of two previous publications by the same authors. We consider the case of two disconnected regions and find that the change in the entanglement entropy depends only on the combined size of the regions and is independent of their connectivity. We subsequently generalize this result to any number of disconnected regions. For the replica negativity we find that its increment is a polynomial with integer coefficients depending only on the sizes of the two regions. The logarithmic negativity turns out to have a more complicated functional structure than its replica version, typically involving roots of polynomials on the sizes of the regions. We obtain our results by two methods already employed in previous work: from a qubit picture and by computing four-point functions of branch point twist fields in finite volume. We test our results against numerical simulations on a harmonic chain and find excellent agreement

Tricritical point of J1-J2 Ising model on hyperbolic lattice

A ferromagnetic-paramagnetic phase transition of the two-dimensional frustrated Ising model on a hyperbolic lattice is investigated by use of the corner transfer matrix renormalization group method. The model contains ferromagnetic nearest-neighbor interaction J_1 and the competing antiferromagnetic interaction J_2. A mean-field like second-order phase transition is observed when the ratio \kappa = J_2 / J_1 is less than 0.203. In the region 0.203 < \kappa < 1/4, the spontaneous magnetization is discontinuous at the transition temperature. Such tricritical behavior suggests that the phase transitions on hyperbolic lattices need not always be mean-field like.Comment: 7 pages, 13 figures, submitted to Phys. Rev.

Direct Imaging of Multiple Planets Orbiting the Star HR 8799

Direct imaging of exoplanetary systems is a powerful technique that can reveal Jupiter-like planets in wide orbits, can enable detailed characterization of planetary atmospheres, and is a key step towards imaging Earth-like planets. Imaging detections are challenging due to the combined effect of small angular separation and large luminosity contrast between a planet and its host star. High-contrast observations with the Keck and Gemini telescopes have revealed three planets orbiting the star HR 8799, with projected separations of 24, 38, and 68 astronomical units. Multi-epoch data show counter-clockwise orbital motion for all three imaged planets. The low luminosity of the companions and the estimated age of the system imply planetary masses between 5 and 13 times that of Jupiter. This system resembles a scaled-up version of the outer portion of our Solar System.Comment: 30 pages, 5 figures, Research Article published online in Science Express Nov 13th, 200

Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories

We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the line shape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ("temperature dependent gap"). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.Comment: 54 pages, 10 figure