Exploration of relativistic symmetry by the similarity renormalization group

TL;DR

This paper employs the similarity renormalization group to analyze relativistic symmetry in the Dirac Hamiltonian, revealing how pseudospin and spin symmetries emerge and are affected by various interactions.

Contribution

It demonstrates the use of the similarity renormalization group to diagonalize the Dirac Hamiltonian and investigates the origins of pseudospin and spin symmetries in relativistic quantum systems.

Findings

Pseudospin splittings are reduced by spin-orbit and dynamical contributions.

Pseudospin symmetry quality depends on the balance between dynamical effects and spin-orbit interactions.

Spin symmetry in antiparticle spectra is accurately reproduced.

Abstract

The similarity renormalization group is used to transform Dirac Hamiltonian into a diagonal form, which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle. The eigenvalues of the operator are verfied to be in good agreement with that of the original Hamiltonian. Furthermore, the pseudospin symmetry is investigated. It is shown that the pseudospin splittings appearing in the nonrelativistic limit are reduced by the contributions from these terms relating the spin-orbit interactions, added by those relating the dynamical terms, and the quality of pseudospin symmetry origins mainly from the competition of the dynamical effects and the spin-orbit interactions. The spin symmetry of antiparticle spectrum is well reproduced in the present calculations.