Locality and entanglement in bandlimited quantum field theory

TL;DR

This paper explores a bandlimited quantum field theory model using Shannon sampling, revealing a transition in entanglement entropy scaling and showing that field degrees of freedom occupy finite, incompressible spatial volumes.

Contribution

It introduces a Shannon sampling-based ultraviolet cutoff in quantum field theory, demonstrating a transition in entanglement entropy scaling and analyzing the localizability of degrees of freedom.

Findings

Transition from logarithmic to linear entropy scaling in 1+1 dimensions

Field degrees of freedom occupy finite, incompressible spatial volumes

No breaking of translation or rotation invariance

Abstract

We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any one lattice whose average spacing is sufficiently small. We explicitly calculate vacuum entanglement entropies in 1+1 dimension and we find a transition between logarithmic and linear scaling of the entropy, which is the expected 1+1 dimensional analog of the transition from an area to a volume law. We also use entanglement entropy and mutual information as measures to probe in detail the localizability of the field degrees of freedom. We find that, even though neither translation nor rotation invariance are broken, each field degree of freedom occupies an incompressible volume of space, indicating a finite information density.