Disorder operators in 2D Fermi and non-Fermi liquids through multidimensional bosonization

Disorder operators are a type of non-local observables for quantum many-body systems, measuring the fluctuations of symmetry charges inside a region. It has been shown that disorder operators can reveal global aspects of many-body states that are otherwise difficult to access through local measurements. We study disorder operator for U (1) (charge or spin) symmetry in 2D Fermi and non-Fermi liquid states, using the multidimensional bosonization formalism. For a region A, the logarithm of the charge disorder parameter in a Fermi liquid with isotropic interactions scales asympototically as lA lA, with lA being the linear size of the region A. We calculate the proportionality coefficient in terms of Landau parameters of the Fermi liquid theory. We then study models of Fermi surface coupled to gapless bosonic fields realizing non-Fermi liquid states. In a simple spinless model, where the fermion density is coupled to a critical scalar, we find that at the quantum critical point, the scaling behavior of the charge disorder operators is drastically modified to lA ² lA. We also consider the composite Fermi liquid state and argue that the charge disorder operator scales as lA.