A low-energy effective Hamiltonian for Landau quasiparticles

TL;DR

This paper develops a new renormalisation scheme to construct Landau quasiparticles in Fermi fluids, unifying interaction and collision effects into an effective Hamiltonian that captures low-energy physics including superfluidity and transport.

Contribution

It introduces a novel energy cutoff-based renormalisation scheme that unifies Landau interaction and collision amplitudes into an effective Hamiltonian for low-energy Fermi fluid physics.

Findings

Computed zero sound speed as a function of scattering length.

Recovered Gork'ov-Melik Barkhudarov correction to superfluid gap.

Unified low-energy description applicable to normal and superfluid phases.

Abstract

We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme relies on an energy cutoff $\Lambda$ which removes the quasi-resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau interaction function $f$ and the collision amplitude in a single amplitude $\mathcal{A}$ regularized by $\Lambda$. Our effective theory captures all the low-energy physics of Fermi fluids that support Landau quasiparticles, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to an atomic Fermi gas with contact interaction to compute the speed of zero sound in function of the scattering length $a$. We also recover the Gork'ov-Melik Barkhudarov correction to the superfluid gap and critical temperature as a direct consequence of the dressing of particles into Landau quasiparticles.