Contributor info: Dr Giuseppe Di Giulio

Pablo Basteiro, Rathindra Nath Das, Giuseppe Di Giulio, Johanna Erdmenger

SciPost Phys. 15, 218 (2023) · published 30 November 2023 | Toggle abstract · pdf

In view of making progress towards establishing a holographic duality for theories defined on a discrete tiling of the hyperbolic plane, we consider a recently proposed boundary spin chain Hamiltonian with aperiodic couplings that are chosen such as to reflect the inflation rule, i.e. the construction principle, of the bulk tiling. As a remnant of conformal symmetry, the spin degrees of freedom are arranged in multiplets of the dihedral group under which the bulk lattice is invariant. For the boundary Hamiltonian, we use strong-disorder RG techniques and evaluate correlation functions, the entanglement entropy and mutual information for the case that the ground state is in an aperiodic singlet phase. We find that two-point functions decay as a power-law with exponent equal to one. Furthermore, we consider the case that the spin variables transform in the fundamental representation of SO(N), leading to a gapless system, and find that the effective central charge obtained from the entanglement entropy scales as lnN, reflecting the number of local degrees of freedom. We also determine the dependence of this central charge on the parameters specifying the bulk tiling. Moreover, we obtain an analytical expression for the mutual information, according to which there is no phase transition at any finite value of the distance between the two intervals involved.

Giuseppe Di Giulio, René Meyer, Christian Northe, Henri Scheppach, Suting Zhao

SciPost Phys. Core 6, 049 (2023) · published 11 July 2023 | Toggle abstract · pdf

We study the symmetry resolution of the entanglement entropy of an interval in two-dimensional conformal field theories (CFTs), by relating the bipartition to the geometry of an annulus with conformal boundary conditions. In the presence of extended symmetries such as Kac-Moody type current algebrae, symmetry resolution is possible only if the boundary conditions on the annulus preserve part of the symmetry group, i.e. if the factorization map associated with the spatial bipartition is compatible with the symmetry in question. The partition function of the boundary CFT (BCFT) is then decomposed in terms of the characters of the irreducible representations of the symmetry group preserved by the boundary conditions. We demonstrate that this decomposition already provides the symmetry resolution of the entanglement spectrum of the corresponding bipartition. Considering the various terms of the partition function associated with the same representation, or charge sector, the symmetry-resolved Rényi entropies can be derived to all orders in the UV cutoff expansion without the need to compute the charged moments. We apply this idea to the theory of a free massless boson with $U(1)$, $\mathbb{R}$ and $\mathbb{Z}_2$ symmetry.

Anna Paola Caricato, Maurizio Martino, Isabella Oceano, Federica Oliva, Stefania Spagnolo, Gabriele Chiodini, Fabio Bossi, Riccardo De Sangro, Claudio Di Giulio, Danilo Domenici, Giuseppe Finocchiaro, Luca Gennaro Foggetta, Marco Garattini, Andrea Ghigo, Federica Giacchino, Paola Gianotti, Tommaso Spadaro, Eleuterio Spiriti, Clara Taruggi, Elisabetta Vilucchi, Venelin Kozhuharov, Simeon Ivanov, Sevtoslav Ivanov, Radoslav Simeonov, Georgi Georgiev, Fabio Ferrarotto, Emanuele Leonardi, Paolo Valente, Elizabeth Long, Giovanni Organtini, Gabriele Piperno, Mauro Raggi, Salvatore Fiore, Paolo Branchini, Diego Tagnani, Vittoria Capirossi, Federico Pinna, Andre Frankenthal

SciPost Phys. Proc. 12, 050 (2023) · published 4 July 2023 | Toggle abstract · pdf

The Positron Annihilation to Dark Matter Experiment (PADME) uses the positron beam of the DA$\Phi$NE Beam-Test Facility, at the Laboratori Nazionali di Frascati (LNF) to search for a Dark Photon $A'$. The search technique studies the missing mass spectrum of single-photon final states in $e^+e^-\rightarrow A'\gamma$ annihilation in a positron-on-thin-target experiment. This approach facilitates searches for new particles such as long lived Axion-Like-Particles, protophobic X bosons and Dark Higgs. This talk illustrated the scientific program of the experiment and its first physics results. In particular, the measurement of the cross-section of the SM process $e^+e^-\rightarrow \gamma\gamma$ at $\sqrt{s}$=21 MeV was shown.

Pablo Basteiro, Giuseppe Di Giulio, Johanna Erdmenger, Jonathan Karl, René Meyer, Zhuo-Yu Xian

SciPost Phys. 13, 103 (2022) · published 3 November 2022 | Toggle abstract · pdf

We propose a new example of discrete holography that provides a new step towards establishing the AdS/CFT duality for discrete spaces. A class of boundary Hamiltonians is obtained in a natural way from regular tilings of the hyperbolic Poincaré disk, via an inflation rule that allows to construct the tiling using concentric layers of tiles. The models in this class are aperiodic spin chains, whose sequences of couplings are obtained from the bulk inflation rule. We explicitly choose the aperiodic XXZ spin chain with spin 1/2 degrees of freedom as an example. The properties of this model are studied by using strong disorder renormalization group techniques, which provide a tensor network construction for the ground state of this spin chain. This can be regarded as discrete bulk reconstruction. Moreover we compute the entanglement entropy in this setup in two different ways: a discretization of the Ryu-Takayanagi formula and a generalization of the standard computation for the boundary aperiodic Hamiltonian. For both approaches, a logarithmic growth of the entanglement entropy in the subsystem size is identified. The coefficients, i.e. the effective central charges, depend on the bulk discretization parameters in both cases, albeit in a different way.

Sara Murciano, Giuseppe Di Giulio, Pasquale Calabrese

SciPost Phys. 8, 046 (2020) · published 26 March 2020 | Toggle abstract · pdf

We study the symmetry resolved entanglement entropies in gapped integrable lattice models. We use the corner transfer matrix to investigate two prototypical gapped systems with a U(1) symmetry: the complex harmonic chain and the XXZ spin-chain. While the former is a free bosonic system, the latter is genuinely interacting. We focus on a subsystem being half of an infinitely long chain. In both models, we obtain exact expressions for the charged moments and for the symmetry resolved entropies. While for the spin chain we found exact equipartition of entanglement (i.e. all the symmetry resolved entropies are the same), this is not the case for the harmonic system where equipartition is effectively recovered only in some limits. Exploiting the gaussianity of the harmonic chain, we also develop an exact correlation matrix approach to the symmetry resolved entanglement that allows us to test numerically our analytic results.