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Vieri Mastropietro

Publications and source records attributed to Vieri Mastropietro.

At least 19 recordsLinked to original sources
arXiv2026

Nonperturbative Chiral Anomaly Cancellation and Irrelevant Operators

The Chiral anomaly cancellation is perturbatively well understood but its nonperturbative validity in presence of a lattice has remained unproven. We provide a rigorous nonperturbative proof of anomaly cancellation and its universality in a variation of the lattice Kogut-Susskind regularization for the multiflavor Sommerfield model, describing Dirac fermions interacting with a non-compact $\mathrm{U}(1)$ quantum vector field. We identify a novel and general mechanism based on the convergence properties of the renormalized expansion and related to the one leading to universality in topological insulators. Irrelevant lattice operators, despite being suppressed along the RG flow, provide essential contributions to the anomaly cancellation.

hep-th↗
arXiv2026

Incommensurate Twisted Bilayer Graphene: emerging quasi-periodicity and stability

We consider a lattice model of twisted bilayer graphene (TBG) for incommensurate twist angles, focusing on the role of large-momentum-transfer Umklapp terms. These terms, which nearly connect the Fermi points of different layers, are typically neglected in effective continuum descriptions but could, in principle, destroy the Dirac cones; they are indeed closely analogous to those appearing in fermions within quasi-periodic potentials, where they play a crucial role. We prove that, for small but finite interlayer coupling, the semimetallic phase is stable provided the angles belong to a fractal set of large measure (which decreases with the hopping strength) characterized by a number-theoretic Diophantine condition. In particular, this set excludes the (zero measure) commensurate angles. Our method combines a Renormalization Group (RG) analysis of the imaginary-time, zero-temperature Green's functions, with number theoretic properties, and it is similar to the technique used in the Lindstedt series approach to Kolmogorov-Arnold-Moser (KAM) theory. The convergence of the resulting series allows us to rule out non-perturbative effects. The result provides a partial justification of the effective continuum description of TBG in which such large-momentum interlayer hopping processes are neglected.

cond-mat.str-el↗
arXiv2026

Non-perturbative renormalization for lattice massive QED$_2$: the ultraviolet problem

We consider a lattice regularization, preserving Ward Identities (WI) and with a Wilson term, of the Massive QED$_2$, describing a fermion with mass $m$ and charge $\mathsf{e}$ interacting with a vector field with mass $M$, in the regime $m\ll M\ll a^{-1}$ ($a$ being the lattice spacing) which is the suitable one to mimic a realistic 4d massive gauge theory like the Electroweak sector. The presence of the lattice and of the mass $m$ breaks any solvability property. In this paper we prove that the effective action obtained after the integration of the ultraviolet degrees of freedom is expressed by expansions which are convergent for values of the coupling $|\mathsf{e}|\le \mathsf{e}_0$, with $\mathsf{e}_0$ independent on $a$ and $m$, and with cut-off-independent bare parameters. By combining this result with the analysis of the infrared part in previous papers we get a complete construction of the model and a number of properties whose analogous are expected to hold in 4d. The analysis is done by integrating out the bosons and reducing to a fermionic theory; however, with respect to the case with momentum regularizations (which break essential features like the WI), the resulting effective fermionic action has not a simple form and this requires the developments of new methods to get the necessary bounds.

math-ph↗
arXiv2025

The g-2 in the neutral Electroweak model with cutoff: convergent expansion, RG and the Jackiw-Weinberg formula

The prediction of the anomalous gyromagnetic factor of the electron, started with the evaluation of the electromagnetic contribution by Schwinger (1948) and of the weak contribution by Jackiw and Weinberg (1972), is one of the major successes of Quantum Field Theory and the Standard Model. The results obtained truncating the series are in spectacular agreement with experiments. Yet, a mathematical justification and an estimate of the truncation error are problematic, being such series diverging and not asymptotic to any QFT. For a non perturbative result, one has to consider the Standard Model as an effective theory valid up to certain energy scales. In this paper we consider the neutral sector of the Electroweak model with a momentum cutoff; we rigorously prove that the anomalous gyromagnetic factor in the effective regularized theory coincides with the Jackiw-Weinberg result, obtained by the truncation of the formal expansion with no cutoffs (whose sum is not expected to exist), up to a regularization-dependent correction which is subdominant in the weak coupling regime if the cutoff is smaller than the inverse coupling and larger than the boson mass. The proof is based on a convergent expansions and Renormalization Group (RG) methods; cancellations based on exact and approximated symmetries are needed to get lowest order dominance.

math-ph↗
arXiv2025

Non-trivial fixed point of a $ψ^4_d$ fermionic theory, II. Anomalous exponent and scaling operators

We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic $ψ^4_d$ model in $d=1,2,3$ with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the RG sense. The model is defined in terms of a Grassmann functional integral with interaction $V^*$, solving a fixed-point RG equation in the presence of external fields, and a fixed ultraviolet cutoff. We define and construct the field and density scale-invariant response functions, and prove that the critical exponent of the former is the naive one, while that of the latter is anomalous and analytic. We construct the corresponding (almost-)scaling operators, whose two point correlations are scale-invariant up to a remainder term, which decays like a stretched exponential at distances larger than the inverse of the ultraviolet cutoff. Our proof is based on constructive RG methods and, specifically, on a convergent tree expansion for the generating function of correlations, which generalizes the approach developed by three of the authors in a previous publication [A. Giuliani, V. Mastropietro, S. Rychkov, JHEP 01 (2021) 026].

math-ph↗
arXiv2024

Edge transport in Haldane-like models with quasi-periodic disorder

We consider Haldane-like $2d$ topological insulators on the cylinder, in the presence of weak quasi-periodic disorder. We prove that, at large distances, the boundary correlations agree with the correlations of a renormalized, translation-invariant, massless relativistic model in $1+1$ dimensions, multiplied by non-universal oscillatory factors, incommensurate with the lattice spacing. Furthermore, we compute the edge conductance and the edge susceptibility, starting from Kubo formula. We obtain explicit expressions for these response functions, completely determined by the renormalized Fermi velocity of the edge modes. In particular, we prove the quantization of the edge conductance, and the non-universality of the susceptibility. The proof relies on multiscale analysis and rigorous renormalization group methods for quasi-periodic systems, and on lattice Ward identities.

math-ph↗
arXiv2024

Universality in the 2d quasi-periodic Ising model and Harris-Luck irrelevance

We prove that in the 2d Ising Model with a weak bidimensional quasi-periodic disorder in the interaction, the critical behavior is the same as in the non-disordered case, that is the critical exponents for the specific heat and energy-energy correlations are identical and no logarithmic corrections are present. The disorder produces a quasi-periodic modulation of the amplitude of the correlations and a renormalization of the velocities, that is the coefficients of the rescaling of positions, and of the critical temperature. The result establishes the validity of the prediction based on the Harris-Luck criterion and it provides the first rigorous proof of universality in the Ising model in presence of quasi-periodic disorder in both directions and for any angle. Small divisors are controlled assuming a Diophantine condition on the frequencies and convergence of the series is proved by Renormalization Group analysis.

math-ph↗
arXiv2024

Non-perturbative RG for the Weak interaction corrections to the magnetic moment

We analyze, by rigorous Renormalization Group (RG) methods, a Fermi model for Weak forces with a single family of leptons, one massless and the other with mass $m=M e^{-β}$, with $M$ the gauge boson mass, a quartic non-local interaction with coupling $λ^2$ and a momentum cut-off $Λ$. The magnetic moment is written as a series in $λ^2$, with $n$-th coefficients bounded by $C^n ({m^2\over M^2}) β^{2n } ({Λ^2\over M^2})^{(1+0^+)(n-1)}$ if $C$ a constant; this implies convergence and provides non-perturbative bounds on the higher orders contribution. The fact that the magnetic moment is associated to a dimensionally irrelevant quantity requires the implementation of cancellations in the multiscale analysis.

hep-th↗
arXiv2023

Anomaly cancellation condition in lattice effective electroweak theory

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 cut-off, 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.

hep-lat↗
arXiv2023

Vanishing of the anomaly in lattice chiral gauge theory

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.

hep-lat↗
arXiv2022

Multi-Channel Luttinger Liquids at the Edge of Quantum Hall Systems

We consider the edge transport properties of a generic class of interacting quantum Hall systems on a cylinder, in the infinite volume and zero temperature limit. We prove that the large-scale behavior of the edge correlation functions is effectively described by the multi-channel Luttinger model. In particular, we prove that the edge conductance is universal, and equal to the sum of the chiralities of the non-interacting edge modes. The proof is based on rigorous renormalization group methods, that allow to fully take into account the effect of backscattering at the edge. Universality arises as a consequence of the integrability of the emergent multi-channel Luttinger liquid combined with lattice Ward identities for the microscopic $2d$ theory.

math-ph↗
arXiv2022

Nonperturbative renormalization of the lattice Sommerfield vector model

The lattice Sommerfield model, describing a massive vector gauge field coupled to a light fermion in 2d, is an ideal candidate to verify perturbative conclusions. In contrast with continuum exact solutions, we prove that there is no infinite field renormalization, implying the reduction of the degree of the ultraviolet divergence, and that anomalies are non renormalized. Such features are the counterpart of analogue properties at the basis of the Standard model perturbative renormalizability. The results are non-perturbative, in the sense that the averages of gauge invariant observables are expressed in terms of convergent expansions uniformly in the lattice and volume.

hep-th↗
arXiv2021

Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder

We consider a fermionic many body system in Zd 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 $T=0$ the exponential decay of the correlations and the vanishing of the Drude weight, signaling Anderson localization in the ground state. The proof combines Ward Identities, Renormalization Group and KAM Lindstedt series methods.

cond-mat.dis-nn↗
arXiv2021

Gentle introduction to rigorous Renormalization Group: a worked fermionic example

Much of our understanding of critical phenomena is based on the notion of Renormalization Group (RG), but the actual determination of its fixed points is usually based on approximations and truncations, and predictions of physical quantities are often of limited accuracy. The RG fixed points can be however given a fully rigorous and non-perturbative characterization, and this is what is presented here in a model of symplectic fermions with a nonlocal ("long-range") kinetic term depending on a parameter $\varepsilon$ and a quartic interaction. We identify the Banach space of interactions, which the fixed point belongs to, and we determine it via a convergent approximation scheme. The Banach space is not limited to relevant interactions, but it contains all possible irrelevant terms with short-ranged kernels, decaying like a stretched exponential at large distances. As the model shares a number of features in common with $ϕ^4$ or Ising models, the result can be used as a benchmark to test the validity of truncations and approximations in RG studies. The analysis is based on results coming from Constructive RG to which we provide a tutorial and self-contained introduction. In addition, we prove that the fixed point is analytic in $\varepsilon$, a somewhat surprising fact relying on the fermionic nature of the problem.

hep-th↗
arXiv2020

Universality for critical lines for Ising, Vertex and Dimer models

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.

math-ph↗
arXiv2020

Anomaly cancellation condition in an effective non-perturbative electroweak theory

We establish the non-perturbative validity of the gauge anomaly cancellation condition in an effective electroweak theory of massless fermions with finite momentum cut-off and Fermi interaction. The requirement that the current is conserved up to terms smaller than the energy divided by the cut-off scale, which is the natural condition as gauge invariance is only emerging, produces the same constraint on charges as in the Standard Model. The result holds at a non-perturbative level as the functional integrals are expressed by convergent power series expansions and are analytic in a finite domain.

hep-ph↗
arXiv2020

Non-integrable dimers: Universal fluctuations of tilted height profiles

We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer model with plaquette interaction previously analyzed in \cite{A,AL,GMT17a,GMT17b}. By tuning the edge weights, we can impose a non-zero average tilt for the height function, so that the considered models are in general not symmetric under discrete rotations and reflections. In the determinantal case, height fluctuations in the massless (or `liquid') phase scale to a Gaussian log-correlated field and their amplitude is a universal constant, independent of the tilt. When the perturbation strength $λ$ is sufficiently small we prove, by fermionic constructive Renormalization Group methods, that log-correlations survive, with amplitude $A$ that, generically, depends non-trivially and non-universally on $λ$ and on the tilt. On the other hand, $A$ satisfies a universal scaling relation (`Haldane' or `Kadanoff' relation), saying that it equals the anomalous exponent of the dimer-dimer correlation.

math-ph↗