Pseudo R\'enyi Entanglement Entropies For an Excited State and Its Time Evolution in a 2D CFT

TL;DR

This paper explores the behavior of pseudo Rénnyi entanglement entropies for excited states in a 2D free scalar CFT, revealing their complex nature during time evolution and dependence on entangling region location.

Contribution

It introduces the study of second and third pseudo Rénnyi entropies for excited states in a 2D CFT, analyzing their time evolution and complex properties.

Findings

PREE is complex for t ≠ 0 and real at t=0.

PREE depends on the entangling region's position.

PREE behavior varies with time and region shape.

Abstract

In this paper, we investigate the second and third pseudo R\'enyi entanglement entropies (PREE) for a locally excited state $| \psi \rangle $ and its time evolution $| \phi \rangle = e^{- i H t} | \psi \rangle$ in a two-dimensional conformal field theory whose field content is a free massless scalar field. We consider excited states which are constructed by applying primary operators at time $t=0$, on the vacuum state. We study the time evolution of the PREE for an entangling region in the shape of finite and semi-infinite intervals at zero temperature. It is observed that the PREE is always a complex number for $t \neq 0$ and is a pure real number at $t=0$. Moreover, we discuss on its dependence on the location $x_m$ of the center of the entangling region.