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

Loïc Herviou (LPMMC) 

Large symmetries are both a curse (larger Hilbert space) and a boon (large irreducible representations) for numerical studies.
In this presentation, I will discuss the method introduced by T. Botzung and P. Nataf in Phys. Rev. Lett. 132 (2023) to tackle optimally Fermi-Hubbard models with SU(N) symmetries. I will exemplify the drastic speedups in an unconventional thermodynamic limit of both large number of colors and particles, and small number of sites. Using a combination of numerical simulations and analytical computation, we get the exact, finite and zero temperature, phase diagrams with systems including several thousand particles.
If time allows, we will discuss generalization of this approach to other Lie groups and models.

Contact : S. Capponi