SVD Entanglement Entropy of Chiral Dirac Oscillators

TL;DR

This paper applies SVD entanglement entropy to chiral Dirac oscillators, demonstrating its divergence at critical points and comparing it to von Neumann entropy, highlighting its advantages in studying quantum phase transitions.

Contribution

It introduces the application of SVD entanglement entropy to chiral Dirac oscillators, providing new insights and a generalized proof related to Bell states.

Findings

SVD entropy diverges at the critical point.

SVD entropy matches von Neumann entropy in the left-handed regime.

SVD entropy is log2 for Bell states differing by phases.

Abstract

We discuss the SVD entanglement entropy, which has recently come up as a successor to the pseudo entropy. This paper is a first of-its-kind application of SVD entanglement entropy to a system of chiral Dirac oscillators which prove to be a natural system to study the SVD formalism because the two chiral oscillator ground states can be taken as the pre-selected and post-selected states. We argue how this alternative for entanglement entropy is better and more intuitive than the von Neumann one to study quantum phase transition. It is shown that SVD entropy diverges at the critical point, matching von Neumann entropy in the left-handed regime but differing in the right-handed regime. We also provide as an illustrative example, a new generalized proof of the SVD entanglement entropy being log2 for a pair of Bell states that differ from each other by relative phases