  A Fermi-liquid (FL) with spin-orbit coupling (SOC) supports a special type of
collective modes--chiral spin waves--which are oscillations of magnetization
even in the absence of the external magnetic field. We study the chiral spin
waves of a two-dimensional FL in the presence of both the Rashba and
Dresselhaus types of SOC and also subject to the in-plane magnetic field. We
map the system of coupled kinetic equations for the angular harmonics of the
occupation number onto an effective one-dimensional tight-binding model, in
which the lattice sites correspond to angular-momentum channels.
Linear-in-momentum SOC ensures that the effective tight-binding model has only
nearest-neighbor hopping on a bipartite lattice. In this language, the
continuum of spin-flip particle-hole excitations becomes a conduction band of
the lattice model, whereas electron-electron interaction, parameterized by the
harmonics of the Landau function, is mapped onto lattice defects of both
on-site and bond type. Collective modes correspond to bound states formed by
such defects. All the features of the collective-mode spectrum receive natural
explanation in the lattice picture as resulting from the competition between
on-site and bond defects.
