Spontaneously Symmetry-Breaking States in the Attractive SU(N) Hubbard Model

We investigate spontaneously symmetry breaking states in the attractive SU( $N$ ) Hubbard model at half filling. Combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method, we obtain the finite temperature phase diagrams for the superfluid state. When $N>2$ , the second-order phase transition occurs in the weak coupling region, while the first-order phase transition with the hysteresis appears in the strong coupling region. We also discuss the stability of the density wave state and clarify the component dependence of the maximum critical temperature.We investigate spontaneously symmetry breaking states in the attractive SU($N$) Hubbard model at half filling. Combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method, we obtain the finite temperature phase diagrams for the superfluid state. When $N>2$, the second-order phase transition occurs in the weak coupling region, while the first-order phase transition with the hysteresis appears in the strong coupling region. We also discuss the stability of the density wave state and clarify the component dependence of the maximum critical temperature.

arXiv:1612.06384Journal of the Physical Society of JapanFeb 3, 201714 citations

Finite-temperature phase transitions in the SU(N) Hubbard model

大将梁取, Hiromasa Yanatori, 昌久古賀 +1 more

Jan 1, 20160 citations

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

Loïc Herviou, Elodie Campan, Pierre Nataf

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 $UWe 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

arXiv:2601.02590Jan 5, 20260 citations

Rigorous Results on the Ground State of the Attractive SU ( N ) Hubbard Model

Hironobu Yoshida, Hosho Katsura

We study the attractive SU(N) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites N_{A} (N_{B}) in the A (B) sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU(N) quantum number. We also show that the ground state exhibits charge density wave order when |N_{A}-N_{B}| is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.We study the attractive SU(N) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites N_{A} (N_{B}) in the A (B) sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU(N) quantum number. We also show that the ground state exhibits charge density wave order when |N_{A}-N_{B}| is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.

arXiv:2011.02296Physical Review LettersMar 12, 202117 citations

We investigate spontaneously symmetry breaking states in the attractive SU(

N

) Hubbard model at half filling. Combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method, we obtain the finite temperature phase diagrams for the superfluid state. When

N>2

, the second-order phase transition occurs in the weak coupling region, while the first-order phase transition with the hysteresis appears in the strong coupling region. We also discuss the stability of the density wave state and clarify the component dependence of the maximum critical temperature.

\mathbb{Z}_L

symmetry breaking in SU(N) Fermi-Hubbard dots at zero and finite temperature

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