Entanglement entropy of a black hole and isolated horizon

Using Unruh-Verlinde temperature obtained by entropic force, we directly calculate partition functions of quantum field in Schwarzschild spacetime via quantum statistical method and derive the expression of the black hole statistical entropy. In our calculation the lower limit of integral is the location of isolated horizon introduced in loop quantum gravity and the upper limit of integral is infinity. So the obtained entropy is the statistical entropy from isolated horizon to the infinite. In our calculation there are not the cutoff and approximation. The results showed that, as long as proper Immirzi parameters are selected, the entropy obtained by loop quantum gravity is consistent with the quantum statistical entropy outside the black hole horizon. Therefore the black hole entropy is a quantum entanglement entropy outside the isolated horizon.