Person: Tempesta, Piergiulio
Universidad Complutense de Madrid
Faculty / Institute
Now showing 1 - 10 of 29
PublicationGeneralized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies(IOP Publishing, 2016-03) Carrasco, José A.; Finkel Morgenstern, Federico; González López, Artemio; Rodríguez González, Miguel Ángel; Tempesta, PiergiulioWe 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 Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi 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 magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi 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≥3. 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 R^m whose vertices are the weights of the fundamental representation of su(m+1). PublicationOn higher-dimensional superintegrable systems: a new family of classical and quantum Hamiltonian models(IOP Publishing Ltd, 2022-12-16) Rodríguez González, Miguel Ángel; Tempesta, PiergiulioWe introduce a family of n-dimensional Hamiltonian systems which, contain, as special reductions, several superintegrable systems as the Tremblay-Turbiner-Winternitz system, a generalized Kepler potential and the anisotropic harmonic oscillator with Rosochatius terms. We conjecture that there exist special values in the space of parameters, apart from those leading to known cases, for which this new Hamiltonian family is superintegrable. PublicationA duality principle for the multi-block entanglement entropy of free fermion systems(Nature Publishing Group, 2017-09-11) Carrasco, J. A.; Finkel Morgenstern, Federico; González López, Artemio; Tempesta, PiergiulioThe analysis of the entanglement entropy of a subsystem of a one-dimensional quantum system is a powerful tool for unravelling its critical nature. For instance, the scaling behaviour of the entanglement entropy determines the central charge of the associated Virasoro algebra. For a free fermion system, the entanglement entropy depends essentially on two sets, namely the set A of sites of the subsystem considered and the set K of excited momentum modes. In this work we make use of a general duality principle establishing the invariance of the entanglement entropy under exchange of the sets A and K to tackle complex problems by studying their dual counterparts. The duality principle is also a key ingredient in the formulation of a novel conjecture for the asymptotic behavior of the entanglement entropy of a free fermion system in the general case in which both sets A and K consist of an arbitrary number of blocks. We have verified that this conjecture reproduces the numerical results with excellent precision for all the configurations analyzed. We have also applied the conjecture to deduce several asymptotic formulas for the mutual and r-partite information generalizing the known ones for the single block case. PublicationNew computable entanglement monotones from formal group theory(Springer, 2021-10) Carrasco, José; Marmo, Giuseppe; Tempesta, PiergiulioWe present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity functions, due their algebraic properties, is suitable for studying entanglement in many-body systems. Under mild hypotheses, the new measures are computable entanglement monotones. Also, they are composable: their evaluation over tensor products can be entirely computed in terms of the evaluations over each factor, by means of a specific group law. In principle, they might be useful to study separability and (in a future perspective) criticality of mixed states, complementing the role of Renyi's entanglement entropy in the discrimination of conformal sectors for pure states. PublicationHigher Haantjes brackets and integrability(Springer, 2021-11) Tempesta, Piergiulio; Tondo, GiorgioWe propose a new, infinite class of brackets generalizing the Frolicher-Nijenhuis bracket. This class can be reduced to a family of generalized Nijenhuis torsions recently introduced. In particular, the Haantjes bracket, the first example of our construction, is relevant in the characterization of Haantjes moduli of operators. We also prove that the vanishing of a higher-level Nijenhuis torsion of an operator field is a sufficient condition for the integrability of its eigen-distributions. This result (which does not require any knowledge of the spectral properties of the operator) generalizes the celebrated Haantjes theorem. The same vanishing condition also guarantees that the operator can be written, in a local chart, in a block-diagonal form. PublicationCritical behavior of su(1|1) supersymmetric spin chains with long-range interactions(American Physical Society, 2016-06-01) Carrasco, José A.; Finkel Morgenstern, Federico; González López, Artemio; Rodríguez González, Miguel Ángel; Tempesta, PiergiulioWe 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,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi 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. PublicationClassical multiseparable Hamiltonian systems, superintegrability and Haantjes geometry(Elsevier, 2022-01) Reyes Nozaleda, Daniel; Tempesta, Piergiulio; Tondo, GiorgioWe show that the theory of classical Hamiltonian systems admitting separating variables can be formulated in the context of (omega, H ) structures. They are symplectic manifolds en-dowed with a compatible Haantjes algebra H , namely an algebra of (1,1)tensor fields with vanishing Haantjes torsion. A special class of coordinates, called Darboux-Haantjes coor-dinates, will be constructed from the Haantjes algebras associated with a separable sys-tem. These coordinates enable the additive separation of variables of the corresponding Hamilton-Jacobi equation. We shall prove that a multiseparable system admits as many omega H structures as sepa-ration coordinate systems. In particular, we will show that a large class of multiseparable, superintegrable systems, including the Smorodinsky-Winternitz systems and some physi-cally relevant systems with three degrees of freedom, possesses multiple Haantjes struc-tures. (C) 2021 Published by Elsevier B.V. PublicationA new entropy based on a group-theoretical structure(Elsevier Masson, 2016-03) Curado, Evaldo M. F.; Tempesta, Piergiulio; Tsallis, ConstantinoA multi-parametric version of the nonadditive entropy S_q is introduced. This new entropic form, denoted by S_a,b,r, possesses many interesting statistical properties, and it reduces to the entropy S_q for b=0, a=r:=1−q (hence Boltzmann–Gibbs entropy S_BG for b=0, a=r→0). The construction of the entropy S_a,b,r is based on a general group-theoretical approach recently proposed by one of us, Tempesta (2016). Indeed, essentially all the properties of this new entropy are obtained as a consequence of the existence of a rational group law, which expresses the structure of S_a,b,r with respect to the composition of statistically independent subsystems. Depending on the choice of the parameters, the entropy S_a,b,r can be used to cover a wide range of physical situations, in which the measure of the accessible phase space increases say exponentially with the number of particles NN of the system, or even stabilizes, by increasing NN, to a limiting value. This paves the way to the use of this entropy in contexts where the size of the phase space does not increase as fast as the number of its constituting particles (or subsystems) increases. PublicationInformation geometry, complexity measures and data analysis(Multidisciplinary Digital Publishing Institute, 2022-12) Amigó, José M.; Tempesta, Piergiulio PublicationSingularity confinement for matrix discrete Painleve equations(IOP Publishing Ltd, 2014-09) Cassatella-Contra, Giovanni A; Mañas Baena, Manuel; Tempesta, PiergiulioWe study the analytic properties of a matrix discrete system introduced by Cassatella and Manas (2012 Stud. Appl. Math. 128 252-74). The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This paves the way to a generalization of Painleve analysis to discrete matrix models.