Abstract
Constraints on infrared (IR) physics arising from ultraviolet (UV) consistency have provided deep insights into the structure of relativistic quantum field theories. We initiate an analogous programme for quantum mechanical lattice models that naturally arise in condensed matter physics. The quantity of interest will be the retarded Green’s function and we will begin by reviewing how it obeys the Lieb-Robinson bound in position space. We will then show that this implies a domain of analyticity in momentum space similar to that enjoyed by relativistic Green’s functions. Moreover, the locality of lattice interactions implies that the spectral function is exponentially bounded in energy. We use these two properties to bound parameters in low energy phenomenological models such as the Drude Model and non-Fermi liquids.

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