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M. Huerta

Publications and source records attributed to M. Huerta.

14 recordsLinked to original sources
arXiv2020

Reduced density matrix and internal dynamics for multicomponent regions

We find the density matrix corresponding to the vacuum state of a massless Dirac field in two dimensions reduced to a region of the space formed by several disjoint intervals. We calculate explicitly its spectral decomposition. The imaginary powers of the density matrix is a unitary operator implementing an internal time flow (the modular flow). We show that in the case of more than one interval this evolution is non-local, producing both, advance in the causal structure and "teleportation" between the disjoint intervals. However, it only mixes the fields on a finite number of trajectories, one for each interval. As an application of these results we compute the entanglement entropy for the massive multi-interval case in the small mass limit.

hep-th↗
arXiv2010

Entanglement entropy for the n-sphere

We calculate the entanglement entropy for a sphere and a massless scalar field in any dimensions. The reduced density matrix is expressed in terms of the infinitesimal generator of conformal transformations keeping the sphere fixed. The problem is mapped to the one of a thermal gas in a hyperbolic space and solved by the heat kernel approach. The coefficient of the logarithmic term in the entropy for 2 and 4 spacetime dimensions are in accordance with previous numerical and analytical results. In particular, the four dimensional result, together with the one reported by Solodukhin, gives support to the Ryu-Takayanagi holographic anzats. We also find there is no logarithmic contribution to the entropy for odd space time dimensions.

hep-th↗
arXiv2009

Entanglement entropy in free quantum field theory

In this review we first introduce the general methods to calculate the entanglement entropy for free fields, within the Euclidean and the real time formalisms. Then we describe the particular examples which have been worked out explicitly in two, three and more dimensions.

hep-th↗
arXiv2009

Remarks on the entanglement entropy for disconnected regions

Few facts are known about the entanglement entropy for disconnected regions in quantum field theory. We study here the property of extensivity of the mutual information, which holds for free massless fermions in two dimensions. We uncover the structure of the entropy function in the extensive case, and find an interesting connection with the renormalization group irreversibility. The solution is a function on space-time regions which complies with all the known requirements a relativistic entropy function has to satisfy. We show that the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields in dimensions greater than two, and the massive free fields in two dimensions all fail to be exactly extensive, disproving recent conjectures.

hep-th↗
arXiv2008

Entanglement entropy for a Dirac fermion in three dimensions: vertex contribution

In three dimensions there is a logarithmically divergent contribution to the entanglement entropy which is due to the vertices located at the boundary of the region considered. In this work we find the corresponding universal coefficient for a free Dirac field, and extend a previous work in which the scalar case was treated. The problem is equivalent to find the conformal anomaly in three dimensional space where multiplicative boundary conditions for the field are imposed on a plane angular sector. As an intermediate step of the calculation we compute the trace of the Green function of a massive Dirac field in a two dimensional sphere with boundary conditions imposed on a segment of a great circle.

hep-th↗
arXiv2008

A Young Planet Search in Visible and IR Light: DN Tau, V836 Tau, and V827 Tau

In searches for low-mass companions to late-type stars, correlation between radial velocity variations and line bisector slope changes indicates contamination by large starspots. Two young stars demonstrate that this test is not sufficient to rule out starspots as a cause of radial velocity variations. As part of our survey for substellar companions to T Tauri stars, we identified the ~2 Myr old planet host candidates DN Tau and V836 Tau. In both cases, visible light radial velocity modulation appears periodic and is uncorrelated with line bisector span variations, suggesting close companions of several M_Jup in these systems. However, high-resolution, infrared spectroscopy shows that starspots cause the radial velocity variations. We also report unambiguous results for V827 Tau, identified as a spotted star on the basis of both visible light and infrared spectroscopy. Our results suggest that infrared follow up observations are critical for determining the source of radial velocity modulation in young, spotted stars.

astro-ph↗
arXiv2008

Analytic results on the geometric entropy for free fields

The trace of integer powers of the local density matrix corresponding to the vacuum state reduced to a region V can be formally expressed in terms of a functional integral on a manifold with conical singularities. Recently, some progress has been made in explicitly evaluating this type of integrals for free fields. However, finding the associated geometric entropy remained in general a difficult task involving an analytic continuation in the conical angle. In this paper, we obtain this analytic continuation explicitly exploiting a relation between the functional integral formulas and the Chung-Peschel expressions for the density matrix in terms of correlators. The result is that the entropy is given in terms of a functional integral in flat Euclidean space with a cut on V where a specific boundary condition is imposed. As an example we get the exact entanglement entropies for massive scalar and Dirac free fields in 1+1 dimensions in terms of the solutions of a non linear differential equation of the Painleve V type.

hep-th↗
arXiv2007

A finite entanglement entropy and the c-theorem

The trace over the degrees of freedom located in a subset of the space transforms the vacuum state into a mixed density matrix with non zero entropy. This is usually called entanglement entropy, and it is known to be divergent in quantum field theory (QFT). However, it is possible to define a finite quantity F(A,B) for two given different subsets A and B which measures the degree of entanglement between their respective degrees of freedom. We show that the function F(A,B) is severely constrained by the Poincare symmetry and the mathematical properties of the entropy. In particular, for one component sets in two dimensional conformal field theories its general form is completely determined. Moreover, it allows to prove an alternative entropic version of the c-theorem for 1+1 dimensional QFT. We propose this well defined quantity as the meaningfull entanglement entropy and comment on possible applications in QFT and the black hole evaporation problem.

hep-th↗
arXiv2006

Universal terms for the entanglement entropy in 2+1 dimensions

We show that the entanglement entropy and alpha entropies corresponding to spatial polygonal sets in $(2+1)$ dimensions contain a term which scales logarithmically with the cutoff. Its coefficient is a universal quantity consisting in a sum of contributions from the individual vertices. For a free scalar field this contribution is given by the trace anomaly in a three dimensional space with conical singularities located on the boundary of a plane angular sector. We find its analytic expression as a function of the angle. This is given in terms of the solution of a set of non linear ordinary differential equations. For general free fields, we also find the small-angle limit of the logarithmic coefficient, which is related to the two dimensional entropic c-functions. The calculation involves a reduction to a two dimensional problem, and as a byproduct, we obtain the trace of the Green function for a massive scalar field in a sphere where boundary conditions are specified on a segment of a great circle. This also gives the exact expression for the entropies for a scalar field in a two dimensional de Sitter space.

hep-th↗
arXiv2006

A c-theorem for the entanglement entropy

The combination of the Lorentz symmetry and the strong subadditive property of the entropy leads to a c-theorem for the entanglement entropy in 1+1 dimensions. We present a simple derivation of this theorem and compare the associated c-functions with the Zamolodchikov's ones for the case of free fields. We discuss the various difficulties which obstacle the naive generalizations of the entropic c-theorem to higher dimensions.

cond-mat.stat-mech↗
arXiv2005

Entanglement and alpha entropies for a massive scalar field in two dimensions

We find the analytic expression of the trace of powers of the reduced density matrix on an interval of length L, for a massive boson field in 1+1 dimensions. This is given exactly (except for a non universal factor) in terms of a finite sum of solutions of non linear differential equations of the Painlevé V type. Our method is a generalization of one introduced by Myers and is based on the explicit calculation of quantities related to the Green function on a plane, where boundary conditions are imposed on a finite cut. It is shown that the associated partition function is related to correlators of exponential operators in the Sine-Gordon model in agreement with a result by Delfino et al. We also compute the short and long distance leading terms of the entanglement entropy. We find that the bosonic entropic c-function interpolates between the Dirac and Majorana fermion ones given in a previous paper. Finally, we study some universal terms for the entanglement entropy in arbitrary dimensions which, in the case of free fields, can be expressed in terms of the two dimensional entropy functions.

cond-mat.other↗
arXiv2005

Entanglement and alpha entropies for a massive Dirac field in two dimensions

We present some exact results about universal quantities derived from the local density matrix, for a free massive Dirac field in two dimensions. We first find the trace of powers of the density matrix in a novel fashion, which involves the correlators of suitable operators in the sine-Gordon model. These, in turn, can be written exactly in terms of the solutions of non-linear differential equations of the Painlevé V type. Equipped with the previous results, we find the leading terms for the entanglement entropy, both for short and long distances, and showing that in the intermediate regime it can be expanded in a series of multiple integrals. The previous results have been checked by direct numerical calculations on the lattice, finding perfect agreement. Finally, we comment on a possible generalization of the entanglement entropy c-theorem to the alpha-entropies.

cond-mat.other↗
arXiv2004

Forbidden Line Emission in the Eccentric Spectroscopic Binaries DQ Tauri and UZ Tauri E Monitored over an Orbital Period

We present echelle spectroscopy of the close pre-main-sequence binary star systems DQ Tau and UZ Tau-E. Over a 16 day time interval we acquired 14 nights of spectra for DQ Tau and 12 nights of spectra for UZ Tau-E. This represents the entire phase of DQ Tau, and 63 percent of the phase of UZ Tau-E. As expected, photospheric lines such as Li I 6707 clearly split into two components as the primary and secondary orbit one another, as did the permitted line He I 5876. Unlike the photospheric features, the forbidden lines of [O I] 6300 and [O I] 5577, retain the same shape throughout the orbit. Therefore these lines must originate outside of the immediate vicinity of the two stars and any circumstellar disks that participate in the orbital motion of the stars.

astro-ph↗