$\mathbb{Z}_L$ symmetry breaking in SU(N) Fermi-Hubbard dots at zero and finite temperature

TL;DR

This paper investigates the SU(N) Fermi-Hubbard model on a chain, demonstrating $Z_L$ symmetry breaking at zero and finite temperature for attractive interactions, with results extending previous work to larger chains and finite temperatures.

Contribution

The study extends previous results on $Z_L$ symmetry breaking in SU(N) Fermi-Hubbard chains to larger chain lengths and finite temperatures using a combination of analytical and numerical methods.

Findings

Ground state degeneracy for U<U_c at T=0

Critical temperature T_c scales with N and U

Symmetry breaking persists at finite temperature for large N

Abstract

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.