Finite Temperature Phase Transitions in the SU$(N)$ Hubbard model

TL;DR

This paper explores finite temperature phase transitions in the SU(N) Hubbard model for multi-component fermionic systems, revealing how component parity influences magnetic ordering and phase transition nature.

Contribution

It combines dynamical mean-field theory with quantum Monte Carlo to map phase diagrams for N≤6, highlighting parity-dependent low-temperature behaviors and phase transition types.

Findings

Magnetically ordered state competes with metallic state for even N

First-order phase transition observed for N≥4

Critical temperature remains constant at strong coupling for odd N

Abstract

We investigate the SU($N$) Hubbard model for the multi-component fermionic optical lattice system, combining dynamical mean-field theory with the continuous-time quantum Monte Carlo method. We obtain the finite temperature phase diagrams with $N\le 6$ and find that low temperature properties depends on the parity of the components. The magnetically ordered state competes with the correlated metallic state in the system with the even number of components $(N\ge 4)$, yielding the first-order phase transition. It is also clarified that, in the odd-component system, the ordered state is realized at relatively lower temperatures and the critical temperature is constant in the strong coupling limit.