Abstract: Lieb-Robinson causality and non-Fermi liquids
Quantum mechanical lattice models with local, bounded interactions obey Lieb-Robinson causality. We show that this implies a domain of analyticity of the retarded Green's function G(ω,k) of local lattice operators as a function of complex frequency ω and momentum k, similar to the lightcone analyticity property of relativistic field theories. Low-energy effective descriptions of the dynamics must be consistent with this microscopic analyticity constraint. In particular, we show that this constraint upper bounds the magnitude of the dimensionless non-Fermi liquid coupling in certain Hertz liquids.