The paper studies a lattice Nambu-Jona-Lasinio (NJL) model with SU(2) and SU(3) flavor symmetries of staggered fermions in the Kogut-Susskind Hamiltonian formalism. The key findings are:
For the spatial dimension ν ≥ 5, the SU(3) model shows a long-range order at sufficiently low temperatures. For the SU(2) symmetry, there appears a long-range order in the spatial dimension ν ≥ 3 at sufficiently low temperatures. These results also hold in the ground states.
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, which are the Nambu-Goldstone modes associated with the spontaneous breakdown of the global rotational symmetry of flavors.
The number of the linearly 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.
The authors use the method of reflection positivity and Gaussian domination to prove the existence of long-range order. They also establish the existence of Nambu-Goldstone modes and show that the number of these modes equals the number of broken symmetry generators.
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by Yukimi Goto,... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2310.15922.pdfDeeper Inquiries