Coalescing hardcore-boson condensate states with nonzero momentum

TL;DR

This paper investigates how non-Hermitian impurities induce the formation of non-zero momentum condensate states in extended Bose-Hubbard systems, revealing the role of exceptional points and boundary scattering dynamics.

Contribution

It provides an exact analysis of condensate states with off-diagonal long-range order influenced by non-Hermitian boundary conditions and exceptional points in bosonic lattice systems.

Findings

Condensate modes with ODLRO can exist under specific parameters.

EPs at boundaries lead to coalescing condensate states with non-zero momentum.

Numerical simulations support the theoretical predictions.

Abstract

Exceptional points (EPs), as an exclusive feature of a non-Hermitian system, support coalescing states to be alternative stable state beyond the ground state. In this work, we explore the influence of non-Hermitian impurities on the dynamic formation of condensate states in one-, two-, and three-dimensional extended Bose-Hubbard systems with strong on-site interaction. Based on the solution for the hardcore limit, we show exactly that condensate modes with off-diagonal long-range order (ODLRO) can exist when certain system parameters satisfy specific matching conditions. Under open boundary conditions, the condensate states become coalescing states when the non-Hermitian $\mathcal{PT}$-symmetric boundary gives rise to the EPs. The fundamental mechanism behind this phenomenon is uncovered through analyzing the scattering dynamics of many-particle wavepackets at the non-Hermitian boundaries. The EP dynamics facilitate the dynamic generation of condensate states with non-zero momentum. To further substantiate the theoretical findings, numerical simulations are conducted. This study not only unveils the potential condensation of interacting bosons but also offers an approach for the engineering of condensate states.