Non-local order in Mott insulators, Duality and Wilson Loops

TL;DR

This paper demonstrates that a non-local parity order parameter can distinguish Mott insulators from superfluids in optical lattices, linking it to gauge theories and Wilson loops, and confirms long-range order in the Mott phase.

Contribution

It introduces a parity order parameter accessible via imaging, relates it to gauge theory Wilson loops, and analyzes its behavior across phases in 1D and 2D systems.

Findings

Parity order exhibits long-range order in 1D Mott insulators.

In 2D, the parity order relates to a Wilson loop with a phase transition.

The parity order parameter follows a perimeter law in the Mott phase.

Abstract

It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local 'parity order parameter' which is directly accessible via single site resolution imaging. In one dimension, the lattice Bose model is dual to a classical interface roughening problem. We use known exact results from the latter to prove that the parity order parameter exhibits long range order in the Mott insulating phase, consistent with recent experiments by Endres et al. [Science 334, 200 (2011)]. In two spatial dimensions, the parity order parameter can be expressed in terms of an equal time Wilson loop of a non-trivial U(1) gauge theory in 2+1 dimensions which exhibits a transition between a Coulomb and a confining phase. The negative logarithm of the parity order parameter obeys a perimeter law in the Mott insulator and is enhanced by a logarithmic factor in the superfluid.