Entanglement of Free Fermions on Johnson Graphs

Free fermions on Johnson graphs $J(n,k)$ are considered and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an analytical expression is provided by the decomposition in irreducible submodules of the Terwilliger algebra of $J(n,k)$ embedded in two copies of $\mathfrak{su}(2)$. For a subsytem composed of multiple neighborhoods, the construction of a block-tridiagonal operator which commutes with the entanglement Hamiltonian is presented, its usefulness in computing the entropy is stressed and the area law pre-factor is discussed.Comment: 24 page

Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes

This study investigates the scaling behavior of the ground-state entanglement entropy in a model of free fermions on folded cubes. An analytical expression is derived in the large-diameter limit, revealing a strict adherence to the area law. The absence of the logarithmic enhancement expected for free fermions is explained using a decomposition of folded cubes in chains based on its Terwilliger algebra and $\mathfrak{so}(3)_{-1}$. The entanglement Hamiltonian and its relation to Heun operators are also investigated.Comment: 19 page

Multipartite information of free fermions on Hamming graphs

We investigate multipartite information and entanglement measures in the ground state of a free-fermion model defined on a Hamming graph. Using the known diagonalization of the adjacency matrix, we solve the model and construct the ground-state correlation matrix. Moreover, we find all the eigenvalues of the chopped correlation matrix when the subsystem consists of $n$ disjoint Hamming subgraphs embedded in a larger one. These results allow us to find an exact formula for the entanglement entropy of disjoint graphs, as well as for the mutual and tripartite information. We use the exact formulas for these measures to extract their asymptotic behavior in two distinct thermodynamic limits, and find excellent match with the numerical calculations. In particular, we find that the entanglement entropy admits a logarithmic violation of the area law which decreases the amount of entanglement compared to the area law scaling.Comment: 12 pages, 4 figures, v2: minor modification

Bethe ansatz diagonalization of the Heun-Racah operator

The Heun-Racah operator is diagonalized with the help of the modified algebraic Bethe ansatz. This operator is the most general bilinear expression in two generators of the Racah algebra. A presentation of this algebra is given in terms of dynamical operators, and allows the construction of Bethe vectors for the Heun-Racah operator. The associated Bethe equations are derived for both the homogeneous and inhomogeneous cases

Quantum State Transfer in Graphs with Tails

We consider quantum state transfer on finite graphs which are attached to infinite paths. The finite graph represents an operational quantum system for performing useful quantum information tasks. In contrast, the infinite paths represent external infinite-dimensional systems which have limited (but nontrivial) interaction with the finite quantum system. We show that {\em perfect} state transfer can surprisingly still occur on the finite graph even in the presence of the infinite tails. Our techniques are based on a decoupling theorem for eventually-free Jacobi matrices, equitable partitions, and standard Lie theoretic arguments. Through these methods, we rehabilitate the notion of a dark subspace which had been so far viewed in an unflattering light.Comment: 25 pages, 7 figure

Les femmes âgées en situation d’itinérance et les trajectoires de désinsertion : y a-t-il des marges de manœuvre?

L’itinérance chez les femmes âgées est un phénomène relativement peu connu, alors que depuis quelques années, on dénote une augmentation de la fréquentation de cette population dans les ressources pour femmes en difficulté et/ou en situation d’itinérance (Conseil des Montréalaises, 2017; CSF, 2012). Ce mémoire cherche à mieux comprendre, par une démarche qualitative, ce qui peut amener les femmes âgées à vivre une situation d’itinérance, en tenant compte de l’influence des facteurs structurels dans l’accélération de leur désinsertion sociale et dans les marges de manœuvre dont elles disposent pour agir sur leur trajectoire. Les données de ce mémoire sont issues de la recherche "Rendre visible l’itinérance au féminin" (Bellot et al., 2015-2017), visant à mieux comprendre les réalités de l’itinérance au féminin. Dans le cadre de cette recherche interrégionale, de nombreuses entrevues ont été réalisées avec des femmes aux histoires et profils variés. De ce corpus, neuf entrevues de type récit de vie réalisées auprès de femmes âgées ayant vécu une situation d’itinérance à partir de l’âge de 50 ans ont été sélectionnées et analysées, en s’appuyant sur la théorie de la désinsertion sociale et sur l’intersectionnalité. Les résultats de ce mémoire démontrent que les femmes âgées vivant une situation d’itinérance font face à des difficultés de logement, de pauvreté, d’isolement social, de violence ainsi qu’à un manque d’adéquation entre leurs besoins et les services et politiques sociales existants. À l’intérieur de ce « décor structurel », les trajectoires sont multiples et variées, déclenchées par divers événements. Souvent avec des marges de manœuvre réduites, les femmes continuent toutefois d’agir et de mettre en place de multiples stratégies pour assurer leur survie et maintenir des conditions de vie acceptables. Les résultats de ce mémoire reflètent la responsabilité étatique dans la mise en place de mesures sociales et politiques adéquates pour répondre aux besoins multiples des femmes âgées en situation d’itinérance, besoins qui ne sont pas comblés dans le respect de leur dignité, étant donné que cette réalité demeure invisible.Homelessness among older women is a relatively unknown phenomenon, despite the fact that an increased attendance of this population in resources for homeless women and/or in difficulty has been witnessed (Conseil des Montréalaises, 2017, CSF, 2012). The qualitative approach of this thesis seeks to better understand what can lead elderly women to experience a situation of homelessness, taking into account the influence of structural factors in accelerating their social exclusion and the room for maneuver they have to act on their trajectory. The data used in this thesis comes from the research "Rendre visible l’itinérance au féminin" (Bellot et al., 2015-2017), which aims to better understand the realities of homeless women. As part of this inter-regional research, several interviews were conducted with women of various backgrounds and profiles. From this body of knowledge, nine life-story interviews with elderly women who experienced homelessness from the age of 50 were selected and analyzed, based on the theory of social exclusion and on intersectionality. The results of this analysis show that older women experiencing homelessness face challenges with housing, poverty, social isolation, violence, and a lack of adequacy between their needs and existing services and social policies. Within this "structural background", the trajectories are multiple and diverse, triggered by various events. However, even with limited room for maneuver, women continue to act and apply many strategies to ensure their survival and to maintain acceptable living conditions. The results of this thesis reflect the state responsibility to put in place appropriate social and political measures that meet the multiple needs of older homeless women – needs which are not currently fulfilled in ways conducive to the preservation of their dignity, given that this reality remains to this day largely invisible