Cauchy–Binet Determinantal Identity and Enumeration of Plane Partitions in a High Box

The amplitudes of the leading asymptotics of the XX 0 Heisenberg spin chain depend on the generating function of plane partitions with the additional conditions. In our paper we apply the Cauchy–Binet determinantal identity for derivation of the generating function of plane partitions with the fixed conjugate trace in a high box.