SU(N) magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations

TL;DR

This paper explores SU(N) Hubbard chains in ultracold alkaline-earth-metal atoms, analyzing phase transitions and quantum correlations using DMRG, Bethe ansatz, and bosonization, and benchmarks their accuracy across different N values.

Contribution

It assesses the validity of Bethe ansatz and strong/weak coupling theories for SU(N) chains and identifies the phase transition point from Luttinger liquid to Mott insulator.

Findings

Bethe ansatz has up to 4% error in ground state energy for N≤4.

The validity of effective models depends weakly on N.

Fidelity susceptibility indicates a phase transition at finite interaction strength for N>2.

Abstract

We investigate one dimensional SU$(N)$ Hubbard chains at zero temperature, which can be emulated with ultracold alkaline earth atoms, by using the density matrix renormalization group (DMRG), Bethe ansatz (BA), and bosonization. We compute experimental observables and use the DMRG to benchmark the accuracy of the Bethe ansatz for $N>2$ where the BA is only approximate. In the worst case, we find a relative error $\epsilon \lesssim 4%$ in the BA ground state energy for $N \leq 4$ at filling 1/N, which is due to the fact that BA improperly treats the triply and higher occupied states. Using the DMRG for $N \leq 4$ and the BA for large $N$, we determine the regimes of validity of strong- and weak-coupling perturbation theory for all values of $N$ and in particular, the parameter range in which the system is well described by a SU$(N)$ Heisenberg model at filling 1/N. We find this depends only weakly on $N$. We investigate the Berezinskii-Kosterlitz-Thouless phase transition from a Luttinger liquid to a Mott-insulator by computing the fidelity susceptibility and the Luttinger parameter $K_\rho$ at 1/N filling. The numerical findings give strong evidence that the fidelity susceptibility develops a minimum at a critical interaction strength which is found to occur at a finite positive value for $N>2$.