Zero modes and divergence of entanglement entropy
Abstract
We investigate the cause of the divergence of the entanglement entropy for the free scalar fields in (1+1) and (D+1) dimensional spacetimes. In a canonically equivalent set of variables, we show explicitly that the divergence in the entanglement entropy of the continuum field in (1+1) dimensions is due to the accumulation of a large number of nearzero frequency modes as opposed to the commonly held view of divergence having UV origin. The feature revealing the divergence in zero modes is related to the observation that the entropy is invariant under a hidden scaling transformation even when the Hamiltonian is not. We discuss the role of dispersion relations and the dimensionality of the spacetime on the behavior of entanglement entropy.
 Publication:

Physical Review D
 Pub Date:
 August 2014
 DOI:
 10.1103/PhysRevD.90.044058
 arXiv:
 arXiv:1404.2079
 Bibcode:
 2014PhRvD..90d4058M
 Keywords:

 04.20.Cv;
 Fundamental problems and general formalism;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 7 pages, 1 figure