Entanglement in quantum field theory via wavelet representations

TL;DR

This paper introduces a wavelet-based multiscale representation for quantum field theories, revealing scale-dependent entanglement and correlations, and demonstrating applications in quantum phase transitions and holography.

Contribution

It presents a novel wavelet-based framework for analyzing quantum field theories, enabling efficient ground state representation and new insights into entanglement and phase transitions.

Findings

Wavelet basis captures scale-dependent entanglement entropy.

Wavelet transform provides a compressed ground state representation.

Application to quantum phase transitions and holographic entanglement.

Abstract

Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free scalar bosonic and Ising model fermionic QFTs using wavelets. Making use of the orthogonality and self similarity of the wavelet basis functions, we demonstrate some well known relations such as scale dependent subsystem entanglement entropy and renormalization of correlations in the ground state. We also find some new applications of the wavelet transform as a compressed representation of ground states of QFTs which can be used to illustrate quantum phase transitions via fidelity overlap and holographic entanglement of purification.