Entanglement entropy in conformal quantum mechanics

TL;DR

This paper explores entanglement entropy in conformal quantum mechanics, linking thermofield double states to observer-dependent temperatures and revealing UV divergences similar to 2D conformal field theories.

Contribution

It introduces a framework connecting conformal quantum mechanics states to observer-dependent thermofield doubles and calculates their entanglement entropy, highlighting UV divergence behavior.

Findings

Entanglement entropy exhibits UV divergent logarithmic behavior.

Thermofield double states correspond to observer-dependent temperatures.

The results mirror known 2D conformal field theory behaviors.

Abstract

We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory. Such states exhibit the structure of a thermofield double built on bipartite eigenstates of generators of non-global time evolution. In terms of the correspondence between radial conformal symmetries in Minkowski spacetime and time evolution in conformal quantum mechanics proposed in arXiv:2002.01836, arXiv:2103.07228, such generators coincide with conformal Killing vectors tangent to worldlines of Milne and diamond observers at constant radius. The temperature of the thermofield double states in conformal quantum mechanics reproduces the temperatures perceived by such diamond and Milne observers. We calculate the entanglement entropy associated to the thermofield double states and obtain a UV divergent logarithmic behaviour analogous to known results in two-dimensional conformal field theory in which the entangling boundary is point-like.