$\mathbb{Z}_L$ symmetry breaking in SU(N) Fermi-Hubbard dots at zero and finite temperature
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arXiv
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| Natura: | Preprint |
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2026
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| _version_ | 1866917186169208832 |
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| author | Herviou, Loïc Campan, Elodie Nataf, Pierre |
| author_facet | Herviou, Loïc Campan, Elodie Nataf, Pierre |
| contents | We address the SU(N) Fermi-Hubbard model on a chain, with $N$ the number of degenerate orbitals, or colors, for each fermion. In the limit of both large number of colors $N$ and particles, and small number of sites $L \geq 2$, the model is proved to undergo a $\mathbb{Z}_L$ symmetry breaking for attractive local interaction amplitude $U$. Using a combination of Exact Diagonalization with full SU(N) symmetry, generalized L-levels Holstein-Primakoff transformation, Hartree-Fock method and large-N saddle point approximation of the partition function, we extend the results obtained in [PRA 111, L020201 (2025)] to $L \geq 3$ and finite temperature $T>0$. In particular, we show that at $T=0$ for $U<U_c\sim -1/N$, the ground state is L-fold degenerate, while for positive temperatures, the critical temperature is both proportional to $N$ and $U$, i.e. $T_c \propto -U N$, making this phase transition particularly suitable for large-N fermions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02590 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $\mathbb{Z}_L$ symmetry breaking in SU(N) Fermi-Hubbard dots at zero and finite temperature Herviou, Loïc Campan, Elodie Nataf, Pierre Strongly Correlated Electrons We address the SU(N) Fermi-Hubbard model on a chain, with $N$ the number of degenerate orbitals, or colors, for each fermion. In the limit of both large number of colors $N$ and particles, and small number of sites $L \geq 2$, the model is proved to undergo a $\mathbb{Z}_L$ symmetry breaking for attractive local interaction amplitude $U$. Using a combination of Exact Diagonalization with full SU(N) symmetry, generalized L-levels Holstein-Primakoff transformation, Hartree-Fock method and large-N saddle point approximation of the partition function, we extend the results obtained in [PRA 111, L020201 (2025)] to $L \geq 3$ and finite temperature $T>0$. In particular, we show that at $T=0$ for $U<U_c\sim -1/N$, the ground state is L-fold degenerate, while for positive temperatures, the critical temperature is both proportional to $N$ and $U$, i.e. $T_c \propto -U N$, making this phase transition particularly suitable for large-N fermions. |
| title | $\mathbb{Z}_L$ symmetry breaking in SU(N) Fermi-Hubbard dots at zero and finite temperature |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2601.02590 |