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.Comment: 4 pages, 1 figur

Coupled identical localized fermionic chains with quasi-random disorder

We analyze the ground state localization properties of an array of identical interacting spinless fermionic chains with quasi-random disorder, using non-perturbative Renormalization Group methods. In the single or two chains case localization persists while for a larger number of chains a different qualitative behavior is generically expected, unless the many body interaction is vanishing. This is due to number theoretical properties of the frequency, similar to the ones assumed in KAM theory, and cancellations due to Pauli principle which in the single or two chains case imply that all the effective interactions are irrelevant; in contrast for a larger number of chains relevant effective interactions are present.Comment: 8 page

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

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

Localization in interacting fermionic chains with quasi-random disorder

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 \cite{M} to chemical potentials outside spectral gaps. The proof is based on Renormalization Group and is inspired by techniques developed to deal with KAM Lindstedt series.Comment: 34 pages, 11 figure

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.Comment: for a special issue of J. Stat. Phys. in memory of Kenneth G. Wilso

Interacting spinning fermions with quasi-random disorder

Interacting spinning fermions with strong quasi-random disorder are analyzed via rigorous Renormalization Group (RG) methods combined with KAM techniques. The correlations are written in terms of an expansion whose convergence follows from number-theoretical properties of the frequency and cancellations due to Pauli principle. A striking difference appears between spinless and spinning fermions; in the first case there are no relevant effective interactions while in presence of spin an additional relevant quartic term is present in the RG flow. The large distance exponential decay of the correlations present in the non interacting case, consequence of the single particle localization, is shown to persist in the spinning case only for temperatures greater than a power of the many body interaction, while in the spinless case this happens up to zero temperature

Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities

We consider the 2D 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. 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.Comment: 4 pages, 1 figure; version published on Phys. Rev. B; erratum adde

Luttinger liquid fixed point for a 2D flat Fermi surface

We consider a system of 2D interacting fermions with a flat Fermi surface. The apparent conflict between Luttinger and non Luttinger liquid behavior found through different approximations is resolved by showing the existence of a line of non trivial fixed points, for the RG flow, corresponding to Luttinger liquid behavior; the presence of marginally relevant operators can cause flow away from the fixed point. The analysis is non-perturbative and based on the implementation, at each RG iteration, of Ward Identities obtained from local phase transformations depending on the Fermi surface side, implying the partial vanishing of the Beta function