Limit cycles in renormalization group dynamics

Bulycheva, Ksenia M.; Gorskii, Aleksandr S.

doi:10.3367/ufnr.0184.201402g.0182

Cited by 4 publications

(2 citation statements)

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“…(18). By substituting κ → − √ m 2 − ǫ 2 and taking the massless limit m → 0, we find an infinite family of complex poles at (30) with multiplicative factors of e π/γ , which leads to…”

Section: Vacuum Polarizationmentioning

confidence: 93%

“…An important point, which seems not to be fully appreciated in previous studies, is that the emergent low-energy parameter r * j is defined only up to multiplicative factors of e π/γ , i.e., e nπ/γ r * j with n being an arbitrary integer corresponds to the same physics. As a consequence, each supercritical channel exhibits the discrete scale invariance, which also emerges in nonrelativistic one-body [25], two-body [27], and three-body [28] problems and can be viewed as a manifestation of the quantum scale anomaly and the renormalization group limit cycle [29,30].…”

Section: Green's Functionmentioning

confidence: 99%

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Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance

Nishida

2014

Phys. Rev. B

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We study massless Dirac fermions in a supercritical Coulomb potential with the emphasis on that its low-energy physics is universal and parametrized by a single quantity per supercritical angular momentum channel. This low-energy parameter with the dimension of length is defined only up to multiplicative factors and thus each supercritical channel exhibits the discrete scale invariance. In particular, we show that the induced vacuum polarization has a power-law tail whose coefficient is a sum of log-periodic functions with respect to the distance from the potential center. This coefficient can also be expressed in terms of the energy and width of so-called atomic collapse resonances. Our universal predictions on the vacuum polarization and its relationship to atomic collapse resonances shed new light on the longstanding fundamental problem of quantum electrodynamics and can in principle be tested by graphene experiments with charged impurities.

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Section: Vacuum Polarizationmentioning

confidence: 93%