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

TL;DR

This paper explores how nonreciprocal hopping in an interacting bosonic chain leads to emergent Mott insulators at noninteger filling and reveals unique non-Hermitian conservation laws affecting quantum dynamics.

Contribution

It introduces a systematic method to identify conservation laws in non-Hermitian many-body systems with real spectra and demonstrates their implications in a specific bosonic chain model.

Findings

Mott insulators can exist at noninteger filling due to nonreciprocal hopping.

Non-Hermitian systems have nonconserved expectation values for operators commuting with the Hamiltonian.

A generic approach to construct conserved quantities in non-Hermitian systems is established.

Abstract

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