Direct mapping of the finite temperature phase diagram of strongly correlated quantum models

TL;DR

This paper introduces a novel experimental method to directly map the finite temperature phase diagram of strongly correlated quantum models, exemplified by the Bose Hubbard model, using only density profiles.

Contribution

The authors propose a new technique to determine phase boundaries from experimental density profiles, enabling phase diagram mapping without relying on extensive numerical simulations.

Findings

Kinks in local compressibility mark phase boundaries.

Method successfully applied to Bose Hubbard model.

Temperature determined from edge density profile.

Abstract

Optical lattice experiments, with the unique potential of tuning interactions and density, have emerged as emulators of nontrivial theoretical models that are directly relevant for strongly correlated materials. However, so far the finite temperature phase diagram has not been mapped out for any strongly correlated quantum model. We propose a remarkable method for obtaining such a phase diagram for the first time directly from experiments using only the density profile in the trap as the input. We illustrate the procedure explicitly for the Bose Hubbard model, a textbook example of a quantum phase transition from a superfluid to a Mott insulator. Using "exact" quantum Monte Carlo simulations in a trap with up to $10^6$ bosons, we show that kinks in the local compressibility, arising from critical fluctuations, demarcate the boundaries between superfluid and normal phases in the trap. The temperature of the bosons in the optical lattice is determined from the density profile at the edge. Our method can be applied to other phase transitions even when reliable numerical results are not available.