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

doi:10.1088/1361-648X/ab9fd4

IMR OpenIR

	The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation
	Xu, Xingran; Liu, Haodi; Zhang, Zhidong; Liang, Zhaoxin
	2020-10-07
发表期刊	JOURNAL OF PHYSICS-CONDENSED MATTER
卷号	32 期号:42
摘要	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 flat band in the context of a polariton condensate. The topological invariants are calculated by both winding numbers in the Brillouin zone and the geometrical phase of Majorana stars on the Bloch sphere. Besides, we provide an intuitive way to study the topological phase transformation with the higher spin, and the flat band offers a platform to define the topological phase transition on the Bloch sphere. According to the trajectories of the Majorana stars, we calculate the geometrical phases of the Majorana stars. We study the Lieb lattice with a complex hopping and find their phases have a jump when the parameters change from the trivial phase to the topological phase. The correlation phase of Majorana stars will rise along with the increase of the imaginary parts of the hopping energy. Besides, we also study the Lieb lattice with different intracell hopping and calculate the geometrical phases of the model using non-Bloch factor under the Majorana's stellar representation. In this case, the correlation phases will always be zero because of the normalized coefficient is always a purely real number and the phase transition is vividly shown with the geometrical phases of the Majorana stars calculated by the mean values of the total phases of both right and the joint left eigenstates.
DOI	10.1088/1361-648X/ab9fd4
WOS记录号	WOS:000555812300001
引用统计	被引频次：6[WOS] [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.imr.ac.cn/handle/321006/155670
专题	中国科学院金属研究所
推荐引用方式 GB/T 7714	Xu, Xingran,Liu, Haodi,Zhang, Zhidong,et al. The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation[J]. JOURNAL OF PHYSICS-CONDENSED MATTER,2020,32(42).
APA	Xu, Xingran,Liu, Haodi,Zhang, Zhidong,&Liang, Zhaoxin.(2020).The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation.JOURNAL OF PHYSICS-CONDENSED MATTER,32(42).
MLA	Xu, Xingran,et al."The non-Hermitian geometrical property of 1D Lieb lattice under Majorana's stellar representation".JOURNAL OF PHYSICS-CONDENSED MATTER 32.42(2020).