Critical points of the three-dimensional Bose-Hubbard model from on-site atom number fluctuations. (arXiv:1903.05936v1 [cond-mat.quant-gas])

We discuss how positions of critical points of the three-dimensional
Bose-Hubbard model can be accurately obtained from variance of the on-site atom
number operator, which can be measured through atom-number-projection
spectroscopy. The idea that we explore is that the derivative of the variance,
with respect to the parameter driving the transition, has a pronounced maximum
close to critical points. We show that Quantum Monte Carlo studies of this
maximum lead to precise determination of critical points for the
superfluid-Mott insulator transition in systems with mean number of atoms per
lattice site equal to one, two, and three. We also extract from such data the
correlation-length critical exponent through the finite-size scaling analysis
and discuss how the derivative of the variance can be reliably computed from
numerical data for the variance. The very same conclusions apply to the
derivative of the nearest-neighbor correlation function, which can be obtained
from routinely measured time-of-flight images.

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