1,721,082 research outputs found
Stability of Weyl semimetals with quasiperiodic disorder
Full text linkWeyl semimetals are phases of matter with excitations effectively described by massless Dirac fermions. Their critical nature makes unclear the persistence of such a phase in the presence of disorder. We present a theorem ensuring the stability of the semimetallic phase in the 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 Kolmogorov-Arnold-Moser theory
Universal Edge Transport in Interacting Hall Systems
Full text linkWe study the edge transport properties of 2d interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the quantization of the edge charge conductance and the bulk-edge correspondence. Instead, the edge Drude weight and the edge susceptibility are interaction-dependent; nevertheless, they satisfy exact universal scaling relations, in agreement with the chiral Luttinger liquid theory. Moreover, charge and spin excitations differ in their velocities, giving rise to the spin–charge separation phenomenon. The analysis is based on exact renormalization group methods, and on a combination of lattice and emergent Ward identities. The invariance of the emergent chiral anomaly under the renormalization group flow plays a crucial role in the proof
Multi-Channel Luttinger Liquids at the Edge of Quantum Hall Systems
Full text linkWe 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 theory.Comment: Extended introduction, minor corrections. 77 page
Anomaly Non-renormalization in Interacting Weyl Semimetals
Full text linkWeyl semimetals are 3D condensed matter systems characterized by a degenerate Fermi surface, consisting of a pair of ‘Weyl nodes’. Correspondingly, in the infrared limit, these systems behave effectively as Weyl fermions in 3+1 dimensions. We consider a class of interacting 3D lattice models for Weyl semimetals and prove that the quadratic response of the quasi-particle flow between the Weyl nodes is universal, that is, independent of the interaction strength and form. Universality is the counterpart of the Adler–Bardeen non-renormalization property of the chiral anomaly for the infrared emergent description, which is proved here in the presence of a lattice and at a non-perturbative level. Our proof relies on constructive bounds for the Euclidean ground state correlations combined with lattice Ward Identities, and it is valid arbitrarily close to the critical point where the Weyl points merge and the relativistic description breaks down
Ward identities and chiral anomaly in the Luttinger liquid
Full text linkSystems of interacting non-relativistic fermions in d =1, as well as spin chains or interacting two dimensional Ising models, verify an hidden approximate Gauge Invariance which can be used to derive suitable Ward Identities. Despite the presence of corrections and anomalies, such Ward Identities can be implemented in a Renormalization Group approach and used to exploit nontrivial cancellations which allow to control the flow of the running coupling constants; in particular this is achieved combining Ward identities, Dyson equations and suitable correction identities for the extra terms appearing in the Ward Identities, due to the presence of cutoffs breaking the local gauge symmetry. The correlations can be computed and show a Luttinger liquid behavior characterized by non-universal critical indices, so that the general Luttinger liquid construction for one dimensional systems is completed without any use of exact solutions. The ultraviolet cutoff can be removed and a Quantum Field Theory corresponding to the Thirring model is also constructed
Canonical Drude Weight for Non-integrable Quantum Spin Chains
Full text linkThe 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
Universality of the Hall conductivity in Interacting electron systems
Full text linkWe prove the quantization of the Hall conductivity for general weakly interacting gapped fermionic systems on two-dimensional periodic lattices. The proof is based on fermionic cluster expansion techniques combined with lattice Ward identities, and on a reconstruction theorem that allows us to compute the Kubo conductivity as the analytic continuation of its imaginary time counterpart
Quantization of the Interacting Hall Conductivity in the Critical Regime
Full text linkThe Haldane model is a paradigmatic 2d lattice model exhibiting the integer quantum Hall effect. We consider an interacting version of the model, and prove that for short-range interactions, smaller than the bandwidth, the Hall conductivity is quantized, for all the values of the parameters outside two critical curves, across which the model undergoes a ‘topological’ phase transition: the Hall coefficient remains integer and constant as long as we continuously deform the parameters without crossing the curves; when this happens, the Hall coefficient jumps abruptly to a different integer. Previous works were limited to the perturbative regime, in which the interaction is much smaller than the bare gap, so they were restricted to regions far from the critical lines. The non-renormalization of the Hall conductivity arises as a consequence of lattice conservation laws and of the regularity properties of the current–current correlations. Our method provides a full construction of the critical curves, which are modified (‘dressed’) by the electron–electron interaction. The shift of the transition curves manifests itself via apparent infrared divergences in the naive perturbative series, which we resolve via renormalization group methods
Nonperturbative RG for the weak interaction corrections to the magnetic moment
No full textWe analyze, by rigorous renormalization group methods, a Fermi model for weak forces with a single family of leptons, one massless and the other with mass m = Me-beta, with M the gauge boson mass, a quartic nonlocal interaction with coupling lambda 2, and a momentum cutoff Lambda. The magnetic moment is written as a series in lambda 2, with n-th coefficients bounded by Cn(m2 M2)beta 2n(M Lambda 2 2)(1+0+)(n-1) if C is a constant; this implies convergence and provides nonperturbative bounds on the higher order contributions. The fact that the magnetic moment is associated with a dimensionally irrelevant quantity requires the implementation of cancellations in the multiscale analysis
Universality and non-universality in the Ashkin-Teller model
No full textGiuseppe Benfatto, Kensuke Yoshida, Francesco Fucit
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