What is the dynamic critical exponent of 2D Fermi liquids?

Momentum conservation combined with the Pauli exclusion principle restricts the available phase space for collisions in the 2D fermion system. At low temperatures, this generically gives rise to a hierarchy of relaxation rates where odd parity Fermi surface deformations are exceptionally long-lived compared to even parity deformations. The interplay between the relaxation of even parity deformations and effectively collisionless odd parity deformations at intermediate time and length scales leads to a so-called "tomographic" regime. We obtain this hierarchy by explicit numerical construction of the linearized interparticle collision operator for fermions in 2D with short-range repulsion. We then compute the dynamic critical exponent from the current autocorrelation function, identifying a plateau in the tomographic regime which is supported over an arbitrarily large window in time at low temperatures and can serve as a dynamical probe of tomographic transport.