Entanglement entropy of SU(3) Yang-Mills theory

Abstract

We calculate the entanglement entropy using a SU(3) quenched lattice gauge simulation. We find that the entanglement entropy scales as $1/l^2$ at small $l$ as in the conformal field theory. Here $l$ is the size of the system, whose degrees of freedom is left after the other part are traced out. The derivative of the entanglement entropy with respect to $l$ hits zero at about $l^{\ast }=0.6\sim 0.7$ [fm] and vanishes above the length. It may imply that the Yang-Mills theory has the mass gap of the order of $1/l^{\ast }$. Within our statistical errors, no discontinuous change can be seen in the entanglement entropy. We discuss also a subtle point appearing in gauge systems when we divide a system with cuts.

Comments: 8 pages, 9 figures, contribution to the "XXVII International Symposium on Lattice Field Theory", July 26-31, 2009, Peking University, Beijing, China