Emergent Mott insulators and non-Hermitian conservation laws in an interacting bosonic chain with noninteger filling and nonreciprocal hopping

We investigate the ground state and quantum dynamics of an interacting bosonic chain with nonreciprocal hopping. In sharp contrast to its Hermitian counterpart, can support Mott insulators in systems noninteger filling due competition between hopping on-site interaction. For dynamics, conservation laws for non-Hermitian manifest a stark difference from their counterpart. particular, any operator that commutes Hamiltonian operator, expectation value is guaranteed be nonconserved dynamics. To systematically identify law, we establish generic approach constructing conserved quantities many-body completely real spectra, illustrate it concretely by system under study. The direct experimental observation performed ultracold atoms optical lattices engineered