arXiv subjects

Vieri Mastropietro

Publications and source records attributed to Vieri Mastropietro.

At least 55 records · Page 3Linked to original sources

arXiv2015

Dense gaps and scaling relations in the interacting Aubry-Andre' model

We study, by rigorous Renormalization Group methods, the interacting Aubry-Andre' model for fermions in the extended regime. We show that the infinitely many gaps of the single particle spectrum persist in presence of weak many body interactions, despite the presence of Umklapp large momentum processes connecting the Fermi points. The width of the gaps is strongly renormalized through critical exponents which verify exact scaling relations.

cond-mat.str-el↗

arXiv2015

Localization of interacting fermions in the Aubry-Andre' model

We consider interacting electrons in a one dimensional lattice with an incommensurate Aubry-Andre' potential in the regime when the single-particle eigenstates are localized. We rigorously establish persistence of ground state localization in presence of weak many-body interaction, for almost all the chemical potentials. The proof uses a quantum many body extension of methods adopted for the stability of tori of nearly integrable hamiltonian systems, and relies on number-theoretic properties of the potential incommensurate frequency.

cond-mat.str-el↗

arXiv2015

Height fluctuations in non-integrable classical dimers

We rigorously establish the asymptotic equivalence between the height function of interacting dimers on the square lattice and the massless Gaussian free field. Our theorem explains the microscopic origin of the sine-Gordon field theory description away from the free fermion point, which has previously been elusive. We use a novel technique, based on the combination of discrete holomorphicity with exact, constructive, renormalization group methods, which has the potential of being applicable to a variety of other non-integrable models at or close to criticality.

cond-mat.stat-mech↗

arXiv2014

Quantum Quench for inhomogeneous states in the non-local Luttinger model

In the Luttinger model with non-local interaction we investigate, by exact analytical methods, the time evolution of an inhomogeneous state with a localized fermion added to the non interacting ground state. In absence of interaction the averaged density has two peaks moving in opposite directions with constant velocities. If the state is evolved with the interacting Hamiltonian two main effects appear. The first is that the peaks have velocities which are not constant but vary between a minimal and maximal value. The second is that a dynamical `Landau quasi-particle weight' appears in the oscillating part of the averaged density, asymptotically vanishing with time, as consequence of the fact that fermions are not excitations of the interacting Hamiltonian.

cond-mat.stat-mech↗

arXiv2014

Localization in an interacting quasi-periodic fermionic chain

We consider a many body fermionic system with an incommensurate external potential and a short range interaction in one dimension. We prove that, for certain densities and weak interactions, the zero temperature thermodynamical correlations are exponentially decaying for large distances, a property indicating persistence of localization in the interacting ground state. The analysis is based on Renormalization Group, and convergence of the renormalized expansion is achieved using fermionic cancellations and controlling the small divisor problem assuming a Diophantine condition for the frequency.

cond-mat.str-el↗

arXiv2014

Weyl semimetallic phase in an interacting lattice system

By using Wilsonian Renormalization Group (RG) methods we rigorously establish the existence of a Weyl semimetallic phase in an interacting three dimensional fermionic lattice system, by showing that the zero temperature Schwinger functions are asymptotically close to the ones of massless Dirac fermions. This is done via an expansion which is convergent in a region of parameters, which includes the quantum critical point discriminating between the semimetallic and the insulating phase.

math-ph↗

arXiv2013

Interacting Weyl semimetals on a lattice

Electron-electron interactions in a Weyl semimetal are rigorously investigated in a lattice model by non perturbative methods. The absence of quantum phase transitions is proved for interactions not too large and short ranged. The anisotropic Dirac cones persist with angles (Fermi velocities) renormalized by the interaction, and with generically shifted Fermi points. As in graphene, the optical conductivity shows universality properties: it is equal to the massless Dirac fermions one with renormalized velocities, up to corrections which are subdominant in modulus.

cond-mat.str-el↗

arXiv2013

Universality, exponents and anomaly cancellation in disordered Dirac fermions

Disordered 2D chiral fermions provide an effective description of several materials including graphene and topological insulators. While previous analysis considered delta correlated disorder and no ultraviolet cut-offs, we consider here the effect of short range correlated disorder and the presence of a momentum cut-off, providing a more realistic description of condensed matter models. We show that the density of states is anomalous with a critical exponent function of the disorder and that conductivity is universal only when the ultraviolet cut-off is removed, as consequence of the supersymmetric cancellation of the anomalies.

cond-mat.dis-nn↗

arXiv2013

Universal conductivity of graphene in the ultra-relativistic regime

We calculate the optical (cutoff >> frequency >> temperature) conductivity in clean graphene in the ultimate low-energy regime, when retardation effects of the electromagnetic interaction become important and when the full Lorentz symmetry emerges. In contrast to what happens with the short range or with the Coulomb long-range instantaneous interactions, the optical conductivity is now no longer equal to its non interacting value, but acquires universal corrections in powers of the fine structure constant. The coefficient of the first order correction is computed, and found to be of order one. We also present the result for the conductivity in the large-N limit, with $N$ as the number of Dirac fermions species, to the order $1/N^2$.

cond-mat.str-el↗

arXiv2013

Conductivity in the Heisenberg chain with next to nearest neighbor interaction

We consider a spin chain given by the XXZ model with a weak next to nearest neighbor perturbation which breaks its exact integrability. We prove that such 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 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.

cond-mat.stat-mech↗

arXiv2013

Universality of one-dimensional Fermi systems, I. Response functions and critical exponents

The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain thermodynamic quantities are expected to be related among each others by model-independent formulas. We establish such relations, the proof of which has represented a challenging mathematical problem, for a general model of spinning fermions on a one dimensional lattice; interactions are short ranged and satisfy a positivity condition which makes the model critical at zero temperature. Proofs are reported in two papers: in the present one, we demonstrate that the zero temperature response functions in the thermodynamic limit are Borel summable and have anomalous power-law decay with multiplicative logarithmic corrections. Critical exponents are expressed in terms of convergent expansions and depend on all the model details. All results are valid for the special case of the Hubbard model.

math-ph↗

arXiv2013

Universality of one-dimensional Fermi systems, II. The Luttinger liquid structure

We complete the proof started in "Universality of one-dimensional Fermi systems, I." of the universal Luttinger liquid relations for a general model of spinning fermions on a lattice, by making use of the Ward Identities due to asymptotically emerging symmetries. This is done by introducing an effective model verifying extra symmetries and by relating its critical exponents to those of the fermion lattice gas by suitable fine tuning of the parameters.

math-ph↗

arXiv2012

Universal finite size corrections and the central charge in non solvable Ising models

We investigate a non solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength λ. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely the fact that at the critical temperature the finite size corrections to the free energy are universal, in the sense that they are exactly independent of the interaction. The corresponding central charge, defined in terms of the coefficient of the first subleading term to the free energy, as proposed by Affleck and Blote-Cardy-Nightingale, is constant and equal to 1/2 for all 0<λ<λ_0 and λ_0 a small but finite convergence radius. This is one of the very few cases where the predictions of CFT can be rigorously verified starting from a microscopic non solvable statistical model. The proof uses a combination of rigorous renormalization group methods with a novel partition function inequality, valid for ferromagnetic interactions.

math-ph↗

arXiv2012

The scaling limit of the energy correlations in non integrable Ising models

We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $λ$, in a scaling limit in which we send the lattice spacing to zero and the temperature to the critical one. Our analysis is based on an exact mapping of the model into an interacting lattice fermionic theory, which generalizes the one originally used by Schultz, Mattis and Lieb for the nearest neighbor Ising model. The interacting model is then analyzed by a multiscale method first proposed by Pinson and Spencer. If the lattice spacing is finite, then the correlations cannot be computed in closed form: rather, they are expressed in terms of infinite, convergent, power series in $λ$. In the scaling limit, these infinite expansions radically simplify and reduce to the limiting energy correlations of the integrable Ising model, up to a finite renormalization of the parameters. Explicit bounds on the speed of convergence to the scaling limit are derived.

math-ph↗

arXiv2011

Exact RG computation of the optical conductivity of graphene

The optical conductivity of a system of electrons on the honeycomb lattice interacting through an electromagnetic field is computed by truncated exact Renormalization Group (RG) methods. We find that the conductivity has the universal value pi/2 times the conductivity quantum up to negligible corrections vanishing as a power law in the limit of low frequencies.

cond-mat.str-el↗

arXiv2011

Lattice quantum electrodynamics for graphene

The effects of gauge interactions in graphene have been analyzed up to now in terms of effective models of Dirac fermions. However, in several cases lattice effects play an important role and need to be taken consistently into account. In this paper we introduce and analyze a lattice gauge theory model for graphene, which describes tight binding electrons hopping on the honeycomb lattice and interacting with a three-dimensional quantum U(1) gauge field. We perform an exact Renormalization Group analysis, which leads to a renormalized expansion that is finite at all orders. The flow of the effective parameters is controlled thanks to Ward Identities and a careful analysis of the discrete lattice symmetry properties of the model. We show that the Fermi velocity increases up to the speed of light and Lorentz invariance spontaneously emerges in the infrared. The interaction produces critical exponents in the response functions; this removes the degeneracy present in the non interacting case and allow us to identify the dominant excitations. Finally we add mass terms to the Hamiltonian and derive by a variational argument the correspondent gap equations, which have an anomalous non-BCS form, due to the non trivial effects of the interaction.

cond-mat.str-el↗

arXiv2011

Universal Luttinger Liquid Relations in the 1D Hubbard Model

We study the 1D extended Hubbard model with a weak repulsive short-range interaction in the non-half-filled band case, using non-perturbative Renormalization Group methods and Ward Identities. At the critical temperature, T = 0, the response functions have anomalous power-law decay with multiplicative logarithmic corrections. The critical exponents, the susceptibility and the Drude weight verify the universal Luttinger liquid relations. Borel summability and (a weak form of) Spin-Charge separation is established.

math-ph↗

arXiv2011

Conductivity between Luttinger liquids: coupled chains and bilayer graphene

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.

cond-mat.str-el↗