paper

Nambu-Goldstone modes in a lattice Nambu-Jona-Lasinio model with multi flavor symmetries

arXiv:2310.15922 · doi:10.1063/5.0218555

Abstract

We study a lattice Nambu-Jona-Lasinio model with SU(2) and SU(3) flavor symmetries of staggered fermions in the Kogut-Susskind Hamiltonian formalism. This type of four-fermion interactions has been widely used for describing low-energy behaviors of strongly interacting quarks as an effective model. In particular, we focus on the Nambu-Goldstone modes associated with the spontaneous breakdown of the flavor symmetries. In the strong coupling regime for the interactions, we prove the following: (i) For the spatial dimension , the SU(3) model shows a long-range order at sufficiently low temperatures. (ii) In the case of the SU(2) symmetry, there appears a long-range order in the spatial dimension at sufficiently low temperatures. (iii) These results hold in the ground states as well. (iv) In general, if a long-range order emerges in this type of models, then there appear gapless excitations above the sector of the infinite-volume ground states. These are nothing but the Nambu-Goldstone modes associated with the spontaneous breakdown of the global rotational symmetry of flavors. (v) In particular, we establish that the number of the lineraly independent Nambu-Goldstone modes is equal to the number of the broken symmetry generators on the Hilbert space constructed from a certain symmetry-breaking infinite-volume ground state.

arXiv comment63 pages, final version to appear in Journal of Mathematical Physics

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