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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2021 Volume 509, Pages 25–38 (Mi znsl7177)

Cauchy–Binet determinantal identity and enumeration of plane partitions in a high box

N. M. Bogoliubov, C. L. Malyshev

St.Petersburg Department of Steklov Institute of Mathematics, RAS, Fontanka 27, St.Petersburg, Russia

Abstract: The amplitudes of the leading asymptotics of the $XX0$ 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.

Key words and phrases: correlation functions, Heisenberg spin chain, plane partitions, Cauchy–Binet determinantal identity.

UDC: 517

Received: 01.12.2021

Language: English



© Steklov Math. Inst. of RAS, 2024