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

TL;DR

This paper introduces a generalized, exactly solvable Bose-Hubbard model with variable geometric multiplicities, enabling comprehensive simulation and classification of Bose-Einstein condensation patterns beyond the standard minimal multiplicity case.

Contribution

It develops a modified linear Bose-Hubbard model that remains exactly solvable for any geometric multiplicity, expanding the scope of BEC phase transition simulations.

Findings

Classified BEC patterns with arbitrary geometric multiplicities.

Provided a complete set of benchmark models for BEC studies.

Enabled exact solutions for generalized Bose-Hubbard models.

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.