Universal thermodynamics of an SU($N$) Fermi-Hubbard Model

TL;DR

This paper investigates the finite-temperature thermodynamics of the SU(N) Fermi-Hubbard model, revealing universal behaviors across different N values at temperatures above the superexchange energy, using advanced numerical methods.

Contribution

It demonstrates that thermodynamic observables in the SU(N) Fermi-Hubbard model exhibit universal N-dependent scaling at high temperatures, supported by numerical and analytical approaches.

Findings

Energy, on-site pairs, and kinetic energy are universal functions of N at high temperatures.

Analytic scaling description is possible using only one- and two-site calculations.

Results extend understanding of SU(N) FHM thermodynamics beyond low-order high-temperature series.

Abstract

The SU(2) symmetric Fermi-Hubbard model (FHM) plays an essential role in strongly correlated fermionic many-body systems. In the one particle per site and strongly interacting limit ${U/t \gg 1}$, it is effectively described by the Heisenberg Hamiltonian. In this limit, enlarging the spin and extending the typical SU(2) symmetry to SU($N$) has been predicted to give exotic phases of matter in the ground state, with a complicated dependence on $N$. This raises the question of what -- if any -- are the finite-temperature signatures of these phases, especially in the currently experimentally relevant regime near or above the superexchange energy. We explore this question for thermodynamic observables by numerically calculating the thermodynamics of the SU($N$) FHM in the two-dimensional square lattice near densities of one particle per site, using determinant Quantum Monte Carlo and Numerical Linked Cluster Expansion. Interestingly, we find that for temperatures above the superexchange energy, where the correlation length is short, the energy, number of on-site pairs, and kinetic energy are universal functions of $N$. Although the physics in the regime studied is well beyond what can be captured by low-order high-temperature series, we show that an analytic description of the scaling is possible in terms of only one- and two-site calculations.