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

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.

published version

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• String and conventional order parameters in the solvable modulated quantum chain
• Constructing Landau framework for topological order: Quantum chains and ladders
• Distinguishing Quantum Phases through Cusps in Full Counting Statistics
• Superconductivity in the Hubbard model: a hidden-order diagnostics from the Luther-Emery phase on ladders
• Magnetic field induced band insulator to Mott insulator transformations in 4-component alkali fermions at half-filling
• Brane order and quantum magnetism in modulated anisotropic ladders
• Measuring Non-local Brane Order with Error-corrected Parity Snapshots
• Nonlocal order parameter of pair superfluids
• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study