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 measurements observables at a finite resolution. We describe multiscale representation free scalar bosonic and Ising model fermionic QFTs wavelets. Making use the orthogonality self-similarity wavelet basis functions, we demonstrate some well-known relations such as scale-dependent subsystem entanglement entropy renormalization correlations ground state. also find new applications transform compressed states which can be used to illustrate quantum phase transitions via fidelity overlap holographic purification.