The infrared limit of the SRG evolution and Levinson's theorem
| dc.contributor.author | Arriola E.R. | |
| dc.contributor.author | Szpigel S. | |
| dc.contributor.author | Timoteo V.S. | |
| dc.date.accessioned | 2024-03-13T01:00:23Z | |
| dc.date.available | 2024-03-13T01:00:23Z | |
| dc.date.issued | 2014 | |
| dc.description.abstract | On a finite momentum grid with N integration points p n and weights wn (n = 1, ..., N) the Similarity Renormalization Group (SRG) with a given generator G unitarily evolves an initial interaction with a cutoff λ on energy differences, steadily driving the starting Hamiltonian in momentum space Hn,m0=pn2δn,m+Vn,m to a diagonal form in the infrared limit (λ→0), Hn,mG,λ→0=Eπ(n)δn,m, where π(n) is a permutation of the eigenvalues E n which depends on G. Levinson's theorem establishes a relation between phase-shifts δ(p n) and the number of bound-states, n B, and reads δ(p1) - δ(p N) = n Bπ. We show that unitarily equivalent Hamiltonians on the grid generate reaction matrices which are compatible with Levinson's theorem but are phase-inequivalent along the SRG trajectory. An isospectral definition of the phase-shift in terms of an energy-shift is possible but requires in addition a proper ordering of states on a momentum grid such as to fulfill Levinson's theorem. We show how the SRG with different generators G induces different isospectral flows in the presence of bound-states, leading to distinct orderings in the infrared limit. While the Wilson generator induces an ascending ordering incompatible with Levinson's theorem, the Wegner generator provides a much better ordering, although not the optimal one. We illustrate the discussion with the nucleon-nucleon (NN) interaction in the S01 and S13 channels. © 2014. | |
| dc.description.firstpage | 149 | |
| dc.description.lastpage | 156 | |
| dc.description.volume | 735 | |
| dc.identifier.doi | 10.1016/j.physletb.2014.06.032 | |
| dc.identifier.issn | 0370-2693 | |
| dc.identifier.uri | https://dspace.mackenzie.br/handle/10899/36376 | |
| dc.relation.ispartof | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | |
| dc.rights | Acesso Aberto | |
| dc.title | The infrared limit of the SRG evolution and Levinson's theorem | |
| dc.type | Artigo | |
| local.scopus.citations | 10 | |
| local.scopus.eid | 2-s2.0-84902662517 | |
| local.scopus.updated | 2024-05-01 | |
| local.scopus.url | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84902662517&origin=inward |