Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via ${\cal PT}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks

• URL: http://arxiv.org/abs/2108.07110v1
• Date: Mon, 16 Aug 2021 14:27:40 GMT
• Title: Bose-Einstein condensation processes with nontrivial geometric multiplicites realized via ${\cal PT}-$symmetric and exactly solvable linear-Bose-Hubbard building blocks
• Abstract summary: It is well known that using the conventional non-Hermitian but $cal PT-$symmetric Bose-Hubbard Hamiltonian with real spectrum one can realize the Bose-Einstein condensation process. 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. 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 $Kgeq 1
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is well known that using the conventional non-Hermitian but ${\cal PT}-$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 $K=1$. 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 $K\geq 1$. 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.

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