  We investigated the behavior of non-Hermitian bosonic gases with Hubbard
interactions in the one-dimensional zigzag optical lattices through the
calculation of dynamic response functions. Our findings showed the existence of
a non-Hermitian quantum phase transition that is dependent on the
pseudo-Hermitian symmetry. The system tends to exhibit a superfluid phase, when
subjected to weak dissipation. While under strong dissipation, the
pseudo-Hermitian symmetry of the system is partially broken, leading to a
transition towards a normal liquid phase. As the dissipation increases beyond
the critical threshold, the pseudo-Hermitian symmetry is completely broken,
resulting in a Mott-insulator phase. We propose an experimental setup using
one-dimensional zigzag optical lattices containing two-electron atoms to
realize this system. Our research emphasizes the key role of non-Hermiticity in
quantum phase transitions and offers a new theoretical framework as well as
experimental methods for understanding the behavior of dissipative quantum
systems, implicating significant development of new quantum devices and
technologies.
