Inferring effective field observables from a discrete model

Understand

A spin system on a lattice can usually be modelled at large scales by an effective quantum field theory.

• A key mathematical result relating the two descriptions is the quantum central limit theorem, which shows that certain spin observables satisfy an algebra of bosonic fields under certain conditions.
• Here, we show that these particular observables and conditions are the relevant ones for an observer with certain limited abilities to resolve spatial locations as well as spin values.
• This is shown by computing the asymptotic behaviour of a quantum Fisher information metric as function of the resolution parameters.