Quantitative determination of the Hubbard model phase diagram from optical lattice experiments by two-parameter scaling

TL;DR

This paper proposes a method using cold atom experiments and two-parameter scaling to accurately map the phase diagram of the Hubbard model across different dimensions.

Contribution

It introduces a novel experimental approach combining finite-size and finite-curvature scaling to determine the Hubbard model phase diagram from optical lattice data.

Findings

Accurate determination of the Mott transition filling with better than 3% error.

Viability demonstrated through simulation in the 1D case.

Method applicable to any dimensionality of the Hubbard model.

Abstract

We propose an experiment to obtain the phase diagram of the fermionic Hubbard model, for any dimensionality, using cold atoms in optical lattices. It is based on measuring the total energy for a sequence of trap profiles. It combines finite-size scaling with an additional `finite-curvature scaling' necessary to reach the homogeneous limit. We illustrate its viability in the 1D case, simulating experimental data in the Bethe-Ansatz local density approximation. Including experimental errors, the filling corresponding to the Mott transition can be determined with better than 3% accuracy.