Bose-Einstein Condensation Processes with Nontrivial Geometric Multiplicities Realized via PT-Symmetric and Exactly Solvable Linear-Bose-Hubbard Building Blocks

Abstract

It is well known that, using the conventional non-Hermitian but (Formula presented.) symmetric Bose-Hubbard Hamiltonian with real spectrum, one can realize the Bose-Einstein condensation (BEC) process in an exceptional-point limit of order N. Such an exactly solvable simulation of the BEC-type phase transition is, unfortunately, incomplete because the standard version of the model only offers an extreme form of the limit, characterized by a minimal geometric multiplicity (Formula presented.). In our paper, we describe a rescaled and partitioned direct-sum modification of the linear version of the Bose-Hubbard model, which remains exactly solvable while admitting any value of (Formula presented.). It offers a complete menu of benchmark models numbered by a specific combinatorial scheme. In this manner, an exhaustive classification of the general BEC patterns with any geometric multiplicity is obtained and realized in terms of an exactly solvable generalized Bose-Hubbard model. © 2021 by the author.