Interaction effects with varying $N$ in SU($N$) symmetric fermion lattice systems

TL;DR

This study non-perturbatively investigates how interaction effects in SU(N) symmetric fermion lattice systems evolve with N, revealing a crossover behavior and N-independent quantities, with implications for ultracold atom experiments.

Contribution

It provides the first non-perturbative analysis of interaction effects across varying N in SU(N) fermion systems, highlighting crossover phenomena and differences between even and odd N.

Findings

Interaction effects are amplified with N in weak coupling.

Increasing N softens the Mott-insulating background in strong coupling.

Certain physical quantities become nearly N-independent in the crossover region.

Abstract

The interaction effects in ultracold Fermi gases with SU($N$) symmetry are studied non-perturbatively in half-filled one-dimensional lattices by employing quantum Monte Carlo simulations.We find that as $N$ increases, weak and strong interacting systems are driven to a crossover region, but from opposite directions as a convergence of itinerancy and Mottness.In the weak interaction region, particles are nearly itinerant,and inter-particle collisions are enhanced by $N$, resulting in the amplification of interaction effects. In contrast, in the strong coupling region, increasing $N$ softens the Mott-insulating background through the enhanced virtual hopping processes.The crossover region exhibits nearly $N$-independent physical quantities, including the relative bandwidth, Fermi distribution, and the spin structure factor.The difference between even-$N$ and odd-$N$ systems is most prominent at small $N$'s with strong interactions, since the odd case allows local real hopping with an energy scale much larger than the virtual one.The above effects can be experimentally tested in ultracold atom experiments with alkaline-earth (-like) fermions such as $^{87}$Sr ($^{173}$Yb).