Entanglement entropy and horizon temperature in conformal quantum mechanics

TL;DR

This paper explores the relationship between entanglement entropy, horizon temperature, and conformal symmetries in quantum mechanics, revealing thermofield double structures and temperature behaviors analogous to known field theory results.

Contribution

It demonstrates that conformal quantum mechanics encodes thermofield double states and reproduces horizon temperatures, linking conformal symmetries to thermodynamic properties of quantum fields.

Findings

Thermofield double structure in conformal quantum mechanics.

Reproduction of diamond and Milne temperatures for specific generators.

Logarithmic UV divergence in entanglement entropy similar to 2D conformal field theory.

Abstract

The generators of radial conformal symmetries in Minkowski space-time can be put in correspondence with generators of time evolution in conformal quantum mechanics. Within this correspondence we show that in conformal quantum mechanics the state corresponding to the inertial vacuum for a conformally invariant field in Minkowski space-time has the structure of a thermofield double. The latter is built from a bipartite "vacuum state" corresponding to the ground state of the generators of hyperbolic time evolution. These can evolve states only within a portion of the time domain. When such generators correspond to conformal Killing vectors mapping a causal diamond in itself and generators of dilations, the temperature of the thermofield double reproduces, respectively, the diamond temperature and the Milne temperature found for massless fields in Minkowski space-time. Moreover, we compute the entanglement entropy associated to the thermofield double states obtaining a UV divergent logarithmic behaviour akin to known results in two-dimensional conformal field theory where the entangling boundary is point-like.