Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su$(1|1)$ supersymmetric spin chains with long-range interactions which includes as particular cases the su$(1|1)$ Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su$(1|1)$ permutation operator, and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low energy excitations and the low temperature behavior of the free energy, which coincides with that of a $(1+1)$-dimensional conformal field theory (CFT) with central charge $c=1$ when the chemical potential lies in the critical interval $(0,\mathcal E(\pi))$, $\mathcal E(p)$ being the dispersion relation. We also analyze the von Neumann and R\'enyi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson $(1+1)$-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge $c=1$. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su$(1|1)$ elliptic chain.Comment: 13 pages, 6 figures, typeset in REVTe

The Radio Jet Associated with the Multiple V380 Ori System

The giant Herbig-Haro object 222 extends over $\sim$6$'$ in the plane of the sky, with a bow shock morphology. The identification of its exciting source has remained uncertain over the years. A non-thermal radio source located at the core of the shock structure was proposed to be the exciting source. However, Very Large Array studies showed that the radio source has a clear morphology of radio galaxy and a lack of flux variations or proper motions, favoring an extragalactic origin. Recently, an optical-IR study proposed that this giant HH object is driven by the multiple stellar system V380 Ori, located about 23$'$ to the SE of HH 222. The exciting sources of HH systems are usually detected as weak free-free emitters at centimeter wavelengths. Here we report the detection of an elongated radio source associated with the Herbig Be star or with its close infrared companion in the multiple V380 Ori system. This radio source has the characteristics of a thermal radio jet and is aligned with the direction of the giant outflow defined by HH~222 and its suggested counterpart to the SE, HH~1041. We propose that this radio jet traces the origin of the large scale HH outflow. Assuming that the jet arises from the Herbig Be star, the radio luminosity is a few times smaller than the value expected from the radio-bolometric correlation for radio jets, confirming that this is a more evolved object than those used to establish the correlation.Comment: 13 pages, 3 figure

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models with su$(m+1)$ spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su$(m+1)$ type. We evaluate in closed form the reduced density matrix of a block of $L$ spins when the whole system is in its ground state, and study the corresponding von Neumann and R\'enyi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as $a\log L$ when $L$ tends to infinity, where the coefficient $a$ is equal to $(m-k)/2$ in the ground state phase with $k$ vanishing su$(m+1)$ magnon densities. In particular, our results show that none of these generalized Lipkin-Meshkov-Glick models are critical, since when $L\to\infty$ their R\'enyi entropy $R_q$ becomes independent of the parameter $q$. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su$(m+1)$ Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when $m-k\ge3$. Finally, in the su$(3)$ case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su$(3)$. This is also true in the su$(m+1)$ case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an $(m+1)$-simplex in $\mathbf R^m$ whose vertices are the weights of the fundamental representation of su$(m+1)$.Comment: Typeset with LaTeX, 32 pages, 3 figures. Final version with corrections and additional reference

Rigidity of equilibrium states and unique quasi-ergodicity for horocyclic foliations

In this paper we prove that for topologically mixing Anosov flows their equilibrium states corresponding to H\"older potentials satisfy a strong rigidity property: they are determined only by their disintegrations on (strong) stable or unstable leaves. As a consequence we deduce: the corresponding horocyclic foliations of such systems are uniquely quasi-ergodic, provided that the corresponding Jacobian is H\"older, without any restriction on the dimension of the invariant distributions. This generalizes a classical result due to Babillott and Ledrappier for the geodesic flow of hyperbolic manifolds. We rely on symbolic dynamics and on recent methods developed by the authors.Comment: 11 page

Geometrical constructions of equilibrium states

In this note we report some advances in the study of thermodynamic formalism for a class of partially hyperbolic system -- center isometries, that includes regular elements in Anosov actions. The techniques are of geometric flavor (in particular, not relying in symbolic dynamics) and even provide new information in the classical case. For such systems, we give in particular a constructive proof of the existence of the SRB measure and of the entropy maximizing measure. It is also established very fine statistical properties (Bernoulliness), and it is given a characterization of equilibrium states in terms of their conditional measures in the stable/unstable lamination, similar to the SRB case. The construction is applied to obtain the uniqueness of quasi-invariant measures associated to H\"older Jacobian for the horocyclic flow.Comment: Announcement of the results in arXiv:2103.07323, arXiv:2103.07333. 10 page