Agradecimentos: E.R.A. would like to thank the Spanish Mineco (Grant FIS2014-59386-P) and Junta de Andalucia (grant FQM225). S.S. and V.S.T. are supported by FAPESP (grant 2014/04975-9). V.S.T. also thanks FAEPEX (grant 1165/2014) and CNPq (grant 310980/2012-7) for financial support

Abstract: We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity...

Abstract: We study the infrared limit of the similarity renormalization group (SRG) using a simple toy model for the nuclear force aiming to investigate the fixed points of the SRG evolution with both the Wilson and the Wegner generators. We show how a fully diagonal interaction at the similarity cutoff lambda -> 0 may be obtained from the eigenvalues of the Hamiltonian and quantify the diagonalness by means of operator norms. While the fixed points for both generators are equivalent when no bound-states are allowed by the interaction, the differences arising from the presence of the Deuteron bound-state can be disentangled very clearly by analyzing the evolved interactions in the infrared limit lambda -> 0 on a finite momentum grid. Another issue we investigate is the location on the diagonal of the Hamiltonian in momentum-space where the SRG evolution places the Deuteron bound-state eigenvalue once it reaches the fixed point. This finite momentum grid setup provides an alternative derivation of the celebrated trace identities, as a by product. The different effects due to either the Wilson or the Wegner generators on the binding energies of A = 2,3,4 systems are investigated and related to the occurrence of a Tjon-line which emerges as the minimum of an avoided crossing between Ea = 4Et - 3Ed and Ea = 2Et. All infrared features of the flow equations are illustrated using the toy model for the two-nucleon S-waves

CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ

310980/2012-7

FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP

2014/04975-9

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