Inferring effective field observables from a discrete model

TL;DR

This paper demonstrates how specific spin observables in lattice models relate to effective quantum field theories by analyzing their asymptotic behaviour through quantum Fisher information, considering resolution limitations.

Contribution

It identifies the relevant observables and conditions for an observer with limited spatial and spin resolution to connect lattice models with effective quantum fields.

Findings

Asymptotic behaviour of quantum Fisher information analyzed

Identifies observables relevant for limited resolution observers

Connects lattice models to quantum field theory under practical constraints

Abstract

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. The relevant observables characterise the state perturbations whose distinguishability does not decay too fast as a function of spatial or spin resolution.