Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric

• URL: http://arxiv.org/abs/2106.09648v2
• Date: Sat, 6 Nov 2021 10:08:33 GMT
• Title: Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• Authors: Yan-Qing Zhu, Wen Zheng, Shi-Liang Zhu, and Giandomenico Palumbo
• Abstract summary: We show that several pseudo-Hermitian phases in two and three dimensions can be built by employing $q$-deformed matrices. We analyze their topological bulk states through non-Hermitian generalizations of Abelian and non-Abelian tensor Berry connections and quantum metric.
• Score: 6.033106259681307
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Among non-Hermitian systems, pseudo-Hermitian phases represent a special class of physical models characterized by real energy spectra and by the absence of non-Hermitian skin effects. Here, we show that several pseudo-Hermitian phases in two and three dimensions can be built by employing $q$-deformed matrices, which are related to the representation of deformed algebras. Through this algebraic approach we present and study the pseudo-Hermitian version of well known Hermitian topological phases, raging from two-dimensional Chern insulators and time-reversal-invariant topological insulators to three-dimensional Weyl semimetals and chiral topological insulators. We analyze their topological bulk states through non-Hermitian generalizations of Abelian and non-Abelian tensor Berry connections and quantum metric. Although our pseudo-Hermitian models and their Hermitian counterparts share the same topological invariants, their band geometries are different. We indeed show that some of our pseudo-Hermitian phases naturally support nearly-flat topological bands, opening the route to the study of pseudo-Hermitian strongly-interacting systems. Finally, we provide an experimental protocol to realize our models and measure the full non-Hermitian quantum geometric tensor in synthetic matter.

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