The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation

Abstract

The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-$1/2$ non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of a three-level Lieb lattice model (or, equivalently, a spin-$1$ non-Hermitian Hamiltonian) with the complex hopping and flat band in the context of a polariton condensate, with the emphasis on the higher spin degree of freedom on topological properties of non-Hermitian Hamiltonian. The topological invariants are calculated by both winding numbers in the Brillouin zone and the geometrical phase of Majorana stars in the Bloch sphere. Besides, we provide an intuitive way to study the topological phase transformation in high dimensions, and the flat band offers a platform to define the high spin topological phase transition on the Bloch sphere. According to the trajectories of the Majorana stars, we calculate the geometrical phases of the Majorana stars, and we find they have a jump when the parameters change from the trivial phase to the topological phase. Besides, the correlation phase of Majorana stars will rise along with the increase of the imaginary parts of the hopping energy.

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Cited by in corpus (4)

• Interaction induced bi-skin effect in an exciton-polariton system
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars