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

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.

7 pages, 3 figures

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• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Full counting statistics in the many-body Hatano-Nelson model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Variational quantum algorithms for scanning the complex spectrum of non-Hermitian systems
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Quantum quench dynamics in the Luttinger liquid phase of the Hatano-Nelson model
• Work statistics and generalized Loschmidt echo for the Hatano-Nelson model
• Emergent non-Hermitian conservation laws at exceptional points
• Exceptional flat bands in bipartite non-Hermitian lattices