Entanglement in quantum field theory via wavelet representations

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 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.

Automated summary

This study introduces a multiscale representation of free scalar bosonic and Ising model fermionic quantum field theories using wavelets. The wavelet transform is shown to reveal scale-dependent subsystem entanglement entropy, renormalization of correlations in the ground state, and serve as a compressed representation of QFT ground states for studying quantum phase transitions.