Post measurement bipartite entanglement entropy in conformal field theories

TL;DR

This paper derives exact formulas for bipartite entanglement entropy after local measurements in 1+1D conformal field theories and verifies them numerically, providing insights into entanglement properties in quantum many-body systems.

Contribution

It presents the first exact analytical formulas for post-measurement bipartite entanglement entropy in 1+1D conformal field theories with boundary conditions.

Findings

Analytical formulas match numerical results in Klein-Gordon and XX chain models.

Established a lower bound for localizable entanglement in harmonic oscillators.

Validated theoretical predictions with high accuracy through numerical checks.

Abstract

We derive exact formulas for bipartite von Neumann entanglement entropy after partial projective local measurement in $1+1$ dimensional conformal field theories with periodic and open boundary conditions. After defining the set up we will check numerically the validity of our results in the case of Klein-Gordon field theory (coupled harmonic oscillators) and spin-$1/2$ XX chain in a magnetic field. The agreement between analytical results and the numerical calculations is very good. We also find a lower bound for localizable entanglement in coupled harmonic oscillators.