A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

Antinucci, Giovanni; Fresta, Luca; Porta, Marcello

doi:10.1007/s00023-020-00909-1

Cited by 4 publications

(5 citation statements)

References 75 publications

(135 reference statements)

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“…The fact that the quadratic response of the axial current to the electromagnetic field divided by the axial renormalization is universal (and not the quadratic response itself, as often stated incorrectly) is the very content of the Adler-Bardeen theorem in massless QED 4 , see the discussion in [1] after Eqs. (6) and (7). Indeed, a naive perturbative computation of the chiral anomaly in QED 4 would apparently give rise to higher order corrections beyond the chiral triangle graph, see [5]: however, as discussed in [1], these corrections are cancelled exactly by the axial vertex renormalization, which is different from the vectorial one.…”

Section: Main Result: Condensed Matter Simulation Of the Chiral Anomalymentioning

confidence: 99%

“…The kernels of the single-scale contribution to the generating function, W (h) (A, A 5 ) satisfy an estimate analogous to (3.74) with n = 0. The combination 7 2…”

Section: Lemma 31 the Following Identities Holdmentioning

confidence: 99%

“…An even more extensive and rapidly growing literature is available on the effects of disorder, which we cannot fully account for here, see[4,61] for a couple of representative results, see also[7,54] for recent rigorous results. Even in that context, the issue of universality of the 'chiral anomaly' for Weyl semi-metals has not been satisfactorily discussed yet.…”

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confidence: 99%

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Anomaly Non-renormalization in Interacting Weyl Semimetals

Giuliani

Mastropietro

Porta

2021

Commun. Math. Phys.

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Weyl 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 $$3+1$$ 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.

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Section: Main Result: Condensed Matter Simulation Of the Chiral Anomalymentioning

confidence: 99%

“…The kernels of the single-scale contribution to the generating function, W (h) (A, A 5 ) satisfy an estimate analogous to (3.74) with n = 0. The combination 7 2…”

Section: Lemma 31 the Following Identities Holdmentioning

confidence: 99%

mentioning

confidence: 99%

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Anomaly Non-renormalization in Interacting Weyl Semimetals

Giuliani

Mastropietro

Porta

2021

Commun. Math. Phys.

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“…The analysis carried out in this paper is inspired by [6], where SUSY and renormalization group have been used to study a massless hierarchical model for disordered three-dimensional semimetals. One of the main obstacles in the control of the oscillatory SUSY integrals for disordered systems is represented by the presence of mostly complex reference Gaussian "measures".…”

Section: Introductionmentioning

confidence: 99%

“…One of the main obstacles in the control of the oscillatory SUSY integrals for disordered systems is represented by the presence of mostly complex reference Gaussian "measures". The extension of [6] to the non-hierarchical case requires the use of a cluster expansion that exploits this strong oscillatory nature of the SUSY integrals.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

Fresta

2021

Math Phys Anal Geom

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We study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

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Analysis of Rural Tourism and Environmental Influencing Factors Based on Analytic Hierarchy Model

Guo

2022

Wireless Communications and Mobile Computing

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This research focuses on the analytic hierarchy model in the decision-making system that has a more complex structure and maintains the stability of the system, models the application process with the complexity and diversity of the rural economy, collects sample data with the help of different types of rural tourism questionnaire surveys, and integrates the data of rural tourism and other tourism into the model. The following are obtained: (1) During the level analysis, each phenotype track uses RRM, C 1 = 0.26 , C 2 = 0.223 , C 3 = 0.52 , C 4 = 0.25 , C 5 = 0.833 , C 6 = 0.442 , C 7 = 0.75 , C 8 = 0.127 , C 9 = 0.876 , C 10 = 0.792 , C 11 = 0.049 , C 12 = 0.16 , C 13 = 0.166 , and C 14 = 0.049 . The problems of the complex structure of the evaluation can be divided into simple analysis modules, and each module is analyzed at a level. The phenotypic trajectory of each individual is divided into target layer, standard layer, and scheme layer. (2) Arrangement and decision modeling were performed according to one or several indicators of different factors. In the hierarchical random regression model, APC = 0.214 , UPUA = 0.042 , TO = 0.081 , YPUA = 0.082 , PCP = 0.068 , and APS = 0.067 . The characteristic quantity analysis of different environments can be carried out, and the amplitude error and frequency error obtained are relatively small. IAND = 0.115 , AVA = 0.198 , RD = 0.119 , PI = 0.041 , PCCL = 0.142 , IOC = 0.201 , and DSTC = 0.069 . The comparison shows that the hierarchical analysis model is better than the hierarchical random regression model. (3) High-efficiency hybrid model correlation acceleration is the worst model. The experimental data are APC = 0.147 , UPUA = 0.029 , TO = 0.055 , YPUA = 0.06 , PCP = 0.047 , APS = 0.046 , IAND = 0.079 , AVA = 0.136 , RD = 0.082 , PI = 0.028 , PCCL = 0.098 , IOC = 0.139 , and DSTC = 0.048 . (4) The predicted 2020 data and the actual data have small errors. The data obtained by the AHP model is GDP = 1262.1 , finance = 185.09 , budget = 68 , tax = 51.92 , fund budget = 69.23 , transfer income = 40.14 , debt income = 7.73 , disposable financial power = 177.37 , fiscal expenditure = 191.26 , public budget = 88.68 , government expenditure = 71.39 , transfer expenditure = 23.46 , debt expenditure = 7.73 , and last year balance = 2.39 .

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A Supersymmetric Hierarchical Model for Weakly Disordered 3d Semimetals

Cited by 4 publications

References 75 publications

Anomaly Non-renormalization in Interacting Weyl Semimetals

Anomaly Non-renormalization in Interacting Weyl Semimetals

Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

Analysis of Rural Tourism and Environmental Influencing Factors Based on Analytic Hierarchy Model

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