Mapping quantum geometry and quantum phase transitions to real space by a fidelity marker

Sousa, Matheus S. M. de; Cruz, Antonio L.; Chen, Wei

doi:10.48550/arxiv.2301.06493

Cited by 1 publication

(1 citation statement)

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“…This is based on the Gauss-Bonnet theorem applied to the topological characterization of the closed Bloch state manifold in the first Brillouin zone, which provides an effective topological index for a class of nontrivial topological phases. [58][59][60][61][62][63][64][65][66][67][68][69][70][71][72] This paper is structured as follows. In Section 2, we study a cyclically modulated SSH model with long-range hopping terms and solve its Hamiltonian in the Bloch momentum space with periodic conditions.…”

Section: Introductionmentioning

confidence: 99%

Quantum geometric tensor and the topological characterization of the extended Su–Schrieffer–Heeger model

Zeng 曾,

Lai 赖,

Wei 魏

et al. 2024

Chinese Phys. B

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We investigate the quantum metric and topological Euler number in a cyclically modulated SuSchrieffer-Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exactly expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the GaussBonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone results in the degeneracy of the quantum metric, which leads to ill-defined noninteger topological Euler numbers. Nevertheless, the non-integer ”Euler number” provides valuable insights and provide an upper bound for absolute values of the Chern numbers.

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