Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study

Field theories of the composite-fermion (CF) metal model it as a Fermi sea of composite fermions coupled to an emergent gauge field. Within the random phase approximation, these theories predict that the Landau damped gauge field leads to a non-analytic correction to the static structure factor S(q) proportional to $q^3\log(q)$. Thanks to the recently developed quaternion formulation for Jain-Kamilla projection[1], we can evaluate the small-q limit of S(q) within CF metal wavefunctions at fillings ν = 1/2 and 1/4 (as well as ν = 1 and 1/3 fillings for bosons) containing as many as N = 900 particles. Our microscopic calculation reveals that S(q) scales as $q^3$ without any log(q) for all studied filling fractions. This behavior can be modeled by a non-interacting Fermi sea of dipolar CFs, which also accurately reproduces the coefficient of the $q^3$ term.

[1]: M. Gattu and J. K. Jain, Unlocking new regimes in fractional quantum hall effect with quaternions, Phys. Rev. Lett. 134, 156501 (2025).