Diagonalization of High-order Second Quantization Form

Abstract

In this letter, by introducing high order tensor representation, the method to diagonalizing second quantization quadratic form is generalized to any orders operators. By some simple calculation and comparison to classic exact diagonalization, this new technique can be verified since has the same result. Moreover, this procedure could also be applied to some analytical computation, which may give some useful information in many-body interacting systems.