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Vieri Mastropietro - One of the best experts on this subject based on the ideXlab platform.

  • Canonical Drude Weight for Non-integrable Quantum Spin Chains
    Journal of Statistical Physics, 2018
    Co-Authors: Vieri Mastropietro, Marcello Porta
    Abstract:

    The Drude weight is a central quantity for the transport properties of quantum spin chains. The canonical definition of Drude weight is directly related to Kubo formula of conductivity. However, the difficulty in the evaluation of such expression has led to several alternative formulations, accessible to different Methods. In particular, the Euclidean, or imaginary-time, Drude weight can be studied via rigorous Renormalization Group. As a result, in the past years several universality results have been proven for such quantity at zero temperature; remarkably, the proofs work for both integrable and non-integrable quantum spin chains. Here we establish the equivalence of Euclidean and canonical Drude weights at zero temperature. Our proof is based on rigorous Renormalization Group Methods, Ward identities, and complex analytic ideas.

  • conductivity in the heisenberg chain with next to nearest neighbor interaction
    Physical Review E, 2013
    Co-Authors: Vieri Mastropietro
    Abstract:

    We consider a spin chain given by the XXZ model with a weak next-to-nearest-neighbor perturbation that breaks its exact integrability. We prove that such a system has an ideal metallic behavior (infinite conductivity), by rigorously establishing strict lower bounds on the zero-temperature Drude weight, which are strictly positive. The proof is based on exact Renormalization Group Methods allowing us to prove the convergence of the expansions and to fully take into account the irrelevant terms, which play an essential role in ensuring the correct lattice symmetries. We also prove that the Drude weight verifies the same parameter-free relations as in the absence of the integrability-breaking perturbation.

  • LUTTINGER MODEL AND LUTTINGER LIQUIDS
    International Journal of Modern Physics B, 2012
    Co-Authors: Vieri Mastropietro
    Abstract:

    The Luttinger model owes its solvability to a number of peculiar features, like its linear relativistic dispersion relation, which are absent in more realistic fermionic systems. Nevertheless according to the Luttinger liquid conjecture a number of relations between exponents and other physical quantities, which are valid in the Luttinger model, are believed to be true in a wide class of systems, including tight binding or jellium one-dimensional fermionic systems. Recently a rigorous proof of several Luttinger liquid relations in nonsolvable models has been achieved; it is based on exact Renormalization Group Methods coming from Constructive Quantum Field Theory and its main steps will be reviewed below.

  • Conductivity between Luttinger liquids: Coupled chains and bilayer graphene
    Physical Review B, 2011
    Co-Authors: Vieri Mastropietro
    Abstract:

    The conductivity properties between Luttinger liquids are analyzed by exact Renormalization Group Methods. We prove that in a two chain system or in a model of bilayer graphene, described by two coupled fermionic honeycomb lattices interacting with a gauge field, the transverse optical conductivity at finite temperature is anomalous and decreasing together with the frequency as a power law with Luttinger liquid exponent.

  • The Two-Dimensional Hubbard Model on the Honeycomb Lattice
    Communications in Mathematical Physics, 2009
    Co-Authors: Alessandro Giuliani, Vieri Mastropietro
    Abstract:

    We consider the two-dimensional (2D) Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analyticity is proved by making use of constructive fermionic Renormalization Group Methods. We show that the interaction produces a modification of the Fermi velocity and of the wave function Renormalization without changing the asymptotic infrared properties of the model with respect to the unperturbed non-interacting case; this rules out the possibility of superconducting or magnetic instabilities in the thermal ground state.

M A Martindelgado - One of the best experts on this subject based on the ideXlab platform.

  • real space Renormalization Group Methods applied to quantum lattice hamiltonians
    LNP, 1997
    Co-Authors: M A Martindelgado
    Abstract:

    I review recent work and some new results, performed in collaboration with G. Sierra, on the Real-Space Renormalization Group method applied to quantum spin lattice systems mainly in spatial dimensions one and two, and to spin ladders which are somehow in between. The first part of these notes is devoted to non-interacting systems in 1D and 2D and the role played by the correlations between blocks. The second part comprises interacting systems in 1D, spin ladders and 2D using the standard BRG method.

  • real space Renormalization Group Methods and quantum Groups
    Physical Review Letters, 1996
    Co-Authors: M A Martindelgado, German Sierra
    Abstract:

    We apply real space Renormalization Group (RG) Methods to study two quantum Group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum Group symmetry is preserved under the RG transformation except for the appearance of a quantum Group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG flow coincides with the tensor product decomposition of cyclic irreducible representations of ${\mathrm{SU}}_{q}\left(2\right)$ with ${q}^{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$.

German Sierra - One of the best experts on this subject based on the ideXlab platform.

  • real space Renormalization Group Methods and quantum Groups
    Physical Review Letters, 1996
    Co-Authors: M A Martindelgado, German Sierra
    Abstract:

    We apply real space Renormalization Group (RG) Methods to study two quantum Group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field (ITF) defined in an open chain with appropriate boundary terms. The quantum Group symmetry is preserved under the RG transformation except for the appearance of a quantum Group anomalous term which vanishes in the classical case. We obtain correctly the line of critical XXZ models. In the ITF model the RG flow coincides with the tensor product decomposition of cyclic irreducible representations of ${\mathrm{SU}}_{q}\left(2\right)$ with ${q}^{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$.

Haru Pinson - One of the best experts on this subject based on the ideXlab platform.

  • Towards a Nonperturbative Renormalization Group Analysis
    Communications in Mathematical Physics, 2008
    Co-Authors: Haru Pinson
    Abstract:

    We prove that a certain class of convex gradient models in high dimensional spaces without the presence of a small parameter renormalizes to a free field. As a consequence we establish a certain asymptotic formula for the partition function. In some ways, this is a realization of Gawedzki and Kupiainen’s idea to use correlation inequalities to augment the rigorous Renormalization Group Methods. We use the more particular suggestion of Spencer to use certain inequalities of Brascamp and Lieb and also the formulation of the correlation functions in terms of the solutions to some partial differential equations given by Helffer and Sjöstrand.

Israel Michael Sigal - One of the best experts on this subject based on the ideXlab platform.

  • Smooth Feshbach map and operator-theoretic Renormalization Group Methods
    Journal of Functional Analysis, 2003
    Co-Authors: Volker Bach, Thomas Chen, Jürg Fröhlich, Israel Michael Sigal
    Abstract:

    Abstract A new variant of the isospectral Feshbach map defined on operators in Hilbert space is presented. It is constructed with the help of a smooth partition of unity, instead of projections, and is therefore called smooth Feshbach map . It is an effective tool in spectral and singular perturbation theory. As an illustration of its power, a novel operator-theoretic Renormalization Group method is described and applied to analyze a general class of Hamiltonians on Fock space. The main advantage of the new Renormalization Group method over its predecessors is its technical simplicity, which it owes to the use of the smooth Feshbach map.