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arXiv:2111.02911 · Physical review. B./Physical review. B

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

Zuo Wang, Li-Jun Lang, Liang He

Published Feb 25, 2022• 18 citations
arXivHTMLPDF

Abstract

We investigate the ground state and quantum dynamics of an interacting bosonic chain with 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.

DOI
10.1103/physrevb.105.054315

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We investigate the ground state and quantum dynamics of an interacting bosonic chain with 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.
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 at non-integer fillings due to the competition between the nonreciprocal hopping and the on-site interaction. For the quantum dynamics, conservation laws for non-Hermitian systems manifest a stark difference from its Hermitian counterpart. In particular, for any Hermitian operator that commutes with the Hamiltonian operator, its expectation value is guaranteed to be non-conserved 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 spectrums, and illustrate it concretely by the system under study. The direct experimental observation of the non-integer-filling Mott insulators and non-Hermitian conservation laws can be performed by ultracold atoms in optical lattices with the engineered nonreciprocal hopping.
Non-Hermitian quantum many-body systems are a fascinating subject to be explored. Using the generalized density matrix renormalization group method and complementary exact diagonalization, we elucidate the many-body ground states and dynamics of a 1D interacting non-Hermitian Aubry-Andr\'e-Harper model for bosons. We find stable ground states in the superfluid and Mott-insulating regimes under wide range of conditions in this model. We reveal a skin superfluid state induced by the non-Hermiticity from the nonreciprocal hopping. We investigate the topology of the Mott-insulating phase and find its independence of the non-Hermiticity. The topological Mott insulators in this non-Hermitian system are characterized by four equal Chern numbers and a quantized shift of biorthogonal many-body polarizations. Furthermore, we show generic asymmetric expansion and correlation dynamics in the system.
We investigate local conserved quantities in non-Hermitian bosonic lattice systems whose underlying Yang--Baxter structure remains unclear. Focusing on a one-dimensional bosonic chain with quartic interactions of creation operators, we provide a new representation of the local conserved quantities previously constructed by Sanatani and Shiraishi. Using Fourier transformation and trigonometric identities, we systematically derive these conserved quantities and show directly that they form a mutually commuting family. We further extend the construction to interactions extending beyond a single site, cubic interactions, asymmetric hopping, and an on-site potential. Our results provide a unified framework for constructing and characterizing local conserved quantities in this class of non-Hermitian many-body systems.
We investigate the dynamical lattice behavior of ultracold bosonic atoms loaded into an optical lattice with two-body dissipation. In the Mott insulating limit, the resulting system can emulate a variety of spin-1/2 non-Hermitian Heisenberg models such as the non-Hermitian Ising, XX, and XXZ models. These different spin models are implemented by tuning the parameter spaces of the hopping amplitude, the loss rates of atoms, and on-site interaction of strength. Moreover, utilizing the improved non-Hermitian density-matrix renormalization group (NH-DMRG) algorithm, we present the correlation functions, Bell nonlocality (B)(\mathcal{B})(B), and quantum Fisher information (QFI) of the non-Hermitian spin systems, where the QFI inversion and order-of-magnitude reduction demonstrate a high sensitivity to the non-Hermitian system parameters. In addition, there exists a parameter space where non-Hermitian and Hermitian systems exhibit the same phase transition behavior as indicated by QFI and B\mathcal{B}B. Our results open a new avenue toward the quantum simulation and observation of non-Hermitian many-body systems.
In this paper, we investigate the quantum phases of two-component bosons in a non-Hermitian optical lattice system featuring a nonreciprocal hopping phase factor. Our analysis focuses on the Bose–Hubbard model in a two-dimensional (2D) square lattice, utilizing the inhomogeneous dynamical Gutzwiller mean-field theory (DGMFT) to examine the ground state. The impact on quantum phases of the inter component interaction varies in the weak-interaction (the inter-component interactions are smaller than intra-component interactions, i.e., [Formula: see text]) and in the strong-interaction (the inter-component interactions are bigger than intra-component interactions, i.e., [Formula: see text]) regime. In the weak regime, we observe a diverse range of quantum phases, including vortex-like liquid, MI islands (the Mott insulator (MI) islands periodically distributed in the superfluid (SF) background) and SF islands (the SF islands periodically distributed in the MI background), and the inter-component counterflow superfluid (CFSF) phases. In the strong regime, we observe phase separation of the two-component bosons.
We investigated the behavior of non-Hermitian bosonic gases with Hubbard interactions in one-dimensional (1D) 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 toward 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 1D zigzag optical lattices containing two-electron atoms to realize this system. In this paper, we emphasize the key role of non-Hermiticity in quantum phase transitions and offer a theoretical framework as well as experimental methods for understanding the behavior of dissipative quantum systems, implicating significant development of quantum devices and technologies.