We study the topological properties of Bose-Mott insulators in one-dimensional non-Hermitian superlattices, which may serve as effective Hamiltonians for cold atomic optical systems with either two-body loss or one-body loss. We find that in the strongly repulsive limit, the Mott insulator states of the Bose-Hubbard model with a finite two-body loss under integer fillings are topological insulators characterized by a finite charge gap, nonzero integer Chern numbers, and nontrivial edge modes in a low-energy excitation spectrum under an open boundary condition. The two-body loss suppressed by the strong repulsion results in a stable topological Bose-Mott insulator which has features similar to the Hermitian case. However, for the non-Hermitian model related to the one-body loss, we find the non-Hermitian topological Mott insulators are unstable with a finite imaginary excitation gap. Finally, we also discuss the stability of the Mott phase in the presence of two-body loss by solving the Lindblad master equation.

Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices

Non-Hermitian Hamiltonians have been extensively studied at the single-particle level. Here, the authors investigate interaction-induced topological Mott insulators in a non-Hermitian fermionic superlattice system, and discover an anomalous boundary effect without its Hermitian counterpart. The interplay of nonreciprocal hopping, superlattice potential, and interactions leads to the absence of edge excitations, defined via only right eigenvectors, of some in-gap states for both the neutral and charge excitation spectra, which can be restored using biorthogonal eigenvectors.

Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices

Non-Hermitian generalizations of the Su-Schrieffer-Heeger (SSH) models with higher periods of the hopping coefficients, called the SSH3 and SSH4 models, are analyzed. The conventional construction of the winding number fails for the Hermitian SSH3 model, but the non-Hermitian generalization leads to a topological system due to a point gap on the complex plane. The non-Hermitian SSH3 model thus has a winding number and exhibits the non-Hermitian skin effect. Moreover, the SSH3 model has two types of localized states and a zero-energy state associated with special symmetries. The total Zak phase of the SSH3 model exhibits quantization, and its finite value indicates coexistence of the two types of localized states. Meanwhile, the SSH4 model resembles the SSH model, and its non-Hermitian generalization also exhibits the non-Hermitian skin effect. A careful analysis of the non-Hermitian SSH4 model with different boundary conditions shows the bulk-boundary correspondence is restored with the help of the generalized Brillouin zone or the real-space winding number. The physics of the non-Hermitian SSH3 and SSH4 models may be tested in various simulators.

https://iopscience.iop.org/article/10.1088/1361-648X/abc974/pdf

Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models.

The study of topological properties by machine learning approaches has attracted considerable interest recently. Here we propose machine learning the topological invariants that are unique in non-Hermitian systems. Specifically, we train neural networks to predict the winding of eigenvalues of four prototypical non-Hermitian Hamiltonians on the complex energy plane with nearly $100%$ accuracy. Our demonstrations in the non-Hermitian Hatano-Nelson model, Su-Schrieffer-Heeger model, and generalized Aubry-Andr\'e-Harper model in one dimension and the two-dimensional Dirac fermion model with non-Hermitian terms show the capability of the neural networks to explore topological invariants and the associated topological phase transitions and topological phase diagrams in non-Hermitian systems. Moreover, the neural networks trained by a small data set in the phase diagram can successfully predict topological invariants in untouched phase regions. Thus, our work paves the way to revealing non-Hermitian topology with the machine learning toolbox.

Machine learning topological invariants of non-Hermitian systems

Recent years have seen remarkable development in open quantum systems effectively described by non-Hermitian Hamiltonians. A unique feature of non-Hermitian topological systems is the skin effect, anomalous localization of an extensive number of eigenstates driven by nonreciprocal dissipation. Despite its significance for non-Hermitian topological phases, the relevance of the skin effect to quantum entanglement and critical phenomena has remained unclear. Here, we find that the skin effect induces a nonequilibrium quantum phase transition in the entanglement dynamics. We show that the skin effect gives rise to a macroscopic flow of particles and suppresses the entanglement propagation and thermalization, leading to the area law of the entanglement entropy in the nonequilibrium steady state. Moreover, we reveal an entanglement phase transition induced by the competition between the unitary dynamics and the skin effect even without disorder or interactions. This entanglement phase transition accompanies nonequilibrium quantum criticality characterized by a nonunitary conformal field theory whose effective central charge is extremely sensitive to the boundary conditions. We also demonstrate that it originates from an exceptional point of the non-Hermitian Hamiltonian and the concomitant scale invariance of the skin modes localized according to the power law. Furthermore, we show that the skin effect leads to the purification and the reduction of von Neumann entropy even in Markovian open quantum systems described by the Lindblad master equation. Our work opens a way to control the entanglement growth and establishes a fundamental understanding of phase transitions and critical phenomena in open quantum systems far from thermal equilibrium.

Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect

Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the Su-Schrieffer-Heeger (SSH) model and discuss its many-body topological Berry phase, which is well defined for all interacting quasi-Hermitian systems (non-Hermitian systems that have real energy spectrum). We then demonstrate that the classification of topological phases for quasi-Hermitian systems is exactly the same as their Hermitian counterparts. Finally, we construct the fixed point partition function for generic 1D interacting non-Hermitian local systems and find that the fixed point partition function still has a one-to-one correspondence to their Hermitian counterparts. Thus, we conclude that the classification of topological phases for generic 1D interacting non-Hermitian systems is still exactly the same as Hermitian systems.

Zhi-Hao Zhang

Papers

Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity.

Classification of topological phases in one dimensional interacting non-Hermitian systems and emergent unitarity