Papers by Vieri Mastropietro
Annales Henri Poincaré, 2002
We consider the half-filled Hubbard model with a cutoff forbidding momenta close to the angles of... more We consider the half-filled Hubbard model with a cutoff forbidding momenta close to the angles of the square shaped Fermi surface. By Renormalization Group methods we find a convergent expansion for the Schwinger function up to exponentially small temperatures. We prove that the system is not a Fermi liquid, but on the contrary it behaves like a Marginal Fermi liquid, a behaviour observed in the normal phase of high T c superconductors.
Annales Henri Poincaré
The anomaly cancellation is a basic property of the Standard Model, crucial for its consistence. ... more The anomaly cancellation is a basic property of the Standard Model, crucial for its consistence. We consider a lattice chiral gauge theory of massless Wilson fermions interacting with a non-compact massive U(1) field coupled with left- and right-handed fermions in four dimensions. We prove in the infinite volume limit, for weak coupling and inverse lattice step of the order of boson mass, that the anomaly vanishes up to subleading corrections and under the same condition as in the continuum. The proof is based on a combination of exact Renormalization Group, non-perturbative decay bounds of correlations and lattice symmetries.
Journal of Mathematical Physics
The anomaly cancellation is at the basis of the perturbative consistence of the Standard Model, a... more The anomaly cancellation is at the basis of the perturbative consistence of the Standard Model, and it provides a partial explanation of charge quantization. We consider an effective electroweak theory on a lattice, with a quartic interaction describing the weak forces and an interaction with the e.m. field. We prove the validity of the anomaly cancellation at a non-perturbative level and with a finite lattice cutoff, even if the lattice breaks some important symmetries, on which perturbative arguments for the cancellation are based. The method of the proof has analogies with the one adopted for establishing the universality in transport of quantum materials.
arXiv (Cornell University), Nov 17, 2020
In planar lattice statistical mechanics models like coupled Ising with quartic interactions, vert... more In planar lattice statistical mechanics models like coupled Ising with quartic interactions, vertex and dimer models, the exponents depend on all the Hamiltonian details. This corresponds, in the Renormalization Group language, to a line of fixed points. A form of universality is expected to hold, implying that all the exponents can be expressed by exact "Kadanoff" relations in terms of a single one of them. This conjecture has been recently established and we review here the key step of the proof, obtained by rigorous Renormalization Group methods and valid irrespectively on the solvability of the model. The exponents are expressed by convergent series in the coupling and, thanks to a set of cancellations due to emerging chiral symmetries, the extended scaling relations are proven to be true.
arXiv (Cornell University), Nov 29, 2021
The anomaly cancellation is at the basis of the perturbative consistence of the Standard Model an... more The anomaly cancellation is at the basis of the perturbative consistence of the Standard Model and it provides a partial explanation of charge quantization. We consider an effective Electroweak theory on a lattice, with a quartic interaction describing the weak forces and an interaction with the e.m. field. We prove the validity of the anomaly cancellation at a non perturbative level and with a finite lattice cutoff , even if the lattice breaks some important symmetries, on which perturbative arguments for the cancellation are based. The method of the proof has analogies with the one adopted for establishing universality in transport of quantum materials.
Journal of Statistical Physics, 2022
We consider a fermionic many body system in $${\mathbb Z}^d$$ Z d with a short range interaction ... more We consider a fermionic many body system in $${\mathbb Z}^d$$ Z d with a short range interaction and quasi-periodic disorder. In the strong disorder regime and assuming a Diophantine condition on the frequencies and on the chemical potential, we prove at $$T=0$$ T = 0 the exponential decay of the correlations and the vanishing of the Drude weight, signaling non-metallic behavior in the ground state. The proof combines Ward Identities, Renormalization Group and KAM Lindstedt series methods.
Physical Review B, 2020
Weyl semimetals are phases of matter with excitations effectively described by massless Dirac fer... more Weyl semimetals are phases of matter with excitations effectively described by massless Dirac fermions. Their critical nature makes unclear the persistence of such phase in presence of disorder. We present a theorem ensuring the stability of the semimetallic phase in presence of weak quasiperiodic disorder. The proof relies on the subtle interplay of the relativistic Quantum Field Theory description combined with number theoretical properties used in KAM theory.
Communications in Mathematical Physics, 2016
We consider a system of fermions with a quasi-random almost-Mathieu disorder interacting through ... more We consider a system of fermions with a quasi-random almost-Mathieu disorder interacting through a many-body short range potential. We establish exponential decay of the zero temperature correlations, indicating localization of the interacting ground state, for weak hopping and interaction and almost everywhere in the frequency and phase; this extends the analysis in [18] to chemical potentials outside spectral gaps. The proof is based on Renormalization Group and it is inspired by techniques developed to deal with KAM Lindstedt series.
Letters in Mathematical Physics, Mar 1, 1999
We study in a rigorous way the XYZ spin model by Renormalization Group methods.
Physical Review B, 2016
We consider the interacting Aubry-André model describing fermions on a one dimensional lattice wi... more We consider the interacting Aubry-André model describing fermions on a one dimensional lattice with an incommensurate potential and a short range many-body interaction. The single particle spectrum has infinitely many gaps in the extended phase and at zero temperature is an insulator for almost all the chemical potentials. The many body interaction has the effect that the gaps are strongly decreased or increased depending on the attractive or repulsive nature of the interaction, but even the smallest gaps remain open. The system is a band-insulator for generic chemical potentials even in presence of interaction and a quantum phase transition is excluded at weak coupling.
Communications in Mathematical Physics, 2015
We consider a one dimensional many body fermionic system with a large incommensurate external pot... more We consider a one dimensional many body fermionic system with a large incommensurate external potential and a weak short range interaction. We prove, for chemical potentials in a gap of the non interacting spectrum, that the zero temperature thermodynamical correlations are exponentially decaying for large distances, with a decay rate much larger than the gap; this indicates the 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.
Physical Review Letters, 2015
We consider interacting electrons in a one-dimensional lattice with an incommensurate Aubry-André... more We consider interacting electrons in a one-dimensional lattice with an incommensurate Aubry-André potential in the regime when the single-particle eigenstates are localized. We rigorously establish the persistence of ground state localization in the 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.
Journal of Statistical Physics, 2014
By using Wilsonian Renormalization Group (RG) methods we rigorously establish the existence of a ... more 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.
We present the first rigorous construction of the QFT Thirring model, for any value of the mass, ... more We present the first rigorous construction of the QFT Thirring model, for any value of the mass, in a functional integral approach, by proving that a set of Grassmann integrals converges, as the cutoffs are removed, to a set of Schwinger functions verifying the Osterwalder-Schrader axioms. The massless limit is investigated and it is shown that the Schwinger functions have different properties with respect to the ones of the well known exact solution: the Ward Identities have anomalies violating the anomaly non-renormalization property and additional anomalies, apparently unnoticed before, are present in the closed equation for the interacting propagator, obtained by combining a Schwinger-Dyson equation with Ward Identities.
Reviews in Mathematical Physics, 1996
This paper consists in a unified exposition of methods and techniques of the renormalization grou... more This paper consists in a unified exposition of methods and techniques of the renormalization group approach to quantum field theory applied to classical mechanics, and in a review of results: (1) a proof of the KAM theorem, by studying the perturbative expansion (Lindstedt series) for the formal solution of the equations of motion; (2) a proof of a conjecture by Gallavotti about the renormalizability of isochronous hamiltonians, i.e. the possibility to add a term depending only on the actions in a hamiltonian function not verifying the anisochrony condition so that the resulting hamiltonian is integrable. Such results were obtained first by Eliasson; however the difficulties arising in the study of the perturbative series are very similar to the problems which one has to deal with in quantum field theory, so that the use of the methods which have been envisaged and developed in the last twenty years precisely in order to solve them allows us to obtain unified proofs, both conceptual...
Physical Review E, 2013
We consider a spin chain given by the XXZ model with a weak next to nearest neighbor perturbation... more 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.
Physical Review B, 2011
The exact vanishing of the interaction corrections to the zero temperature optical conductivity o... more The exact vanishing of the interaction corrections to the zero temperature optical conductivity of undoped graphene in the presence of weak short-range interactions is rigorously established. Our results are in agreement with measurements of graphene's ac conductivity in a range of frequencies between the temperature and the bandwidth. Even if irrelevant in the renormalization group sense, lattice effects and nonlinear bands are essential for the universality of the conductivity.
Physical Review B, 2009
We consider the two-dimensional Hubbard model on the honeycomb lattice, as a model for single lay... more We consider the two-dimensional Hubbard model on the honeycomb lattice, as a model for single layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its non-interacting value and turns out to be isotropic; as a consequence, the Dirac cones are isotropic at low energies. On the contrary, the interaction produces an asymmetry between the two components of the charge velocity, in contrast with the predictions based on relativistic or continuum approximations.
Physical Review B, 2013
We calculate the optical (ω T) conductivity in clean graphene in the ultimate low-energy regime, ... more We calculate the optical (ω T) 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 noninteracting 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 .
Nuclear Physics B, 2013
Disordered 2D chiral fermions provide an effective description of several materials including gra... more 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 cutoffs , we consider here the effect of short range correlated disorder and the presence of a momentum cutoff , 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 cutoff is removed, as consequence of the supersymmetric cancellation of the anomalies.
Uploads
Papers by Vieri Mastropietro