Quantum geometric analysis of non-Hermitian long-range Kitaev chain
Kartik Yalavalli Ramachandra Subray Hegde1*, Jhih-Shih You2, H. H. Jen1,3
1Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan
2Department of Physics, National Taiwan Normal University, Taipei, Taiwan
3Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan
* Presenter:Kartik Yalavalli Ramachandra Subray Hegde, email:yrkartik@gmail.com
Long-range (LR) couplings play a crucial role in understanding the non-local behavior of quantum systems, yet they remain underexplored in the presence of non-Hermitian (NH) interactions. To investigate the interplay between geometry and criticality in NH systems, we introduce a NH-LR extension of the Kitaev chain and analyze its physical properties. Using biorthonormal vector bases, we construct the geometric phase (GP) and quantum geometric tensor (QGT) to probe criticality, exceptional points, and coalescing NH phases. We perform GP scaling to address quantization and the emergence of fractional phases in NH-LR systems. The geometric properties and scaling behavior near exceptional points are studied via the QGT. The Wannier state correlation function (WCF) reveals unconventional behavior around critical points, providing insight into the emergence of a new universality class of critical exponents. Additionally, spectral analysis highlights the dependence of specific criticalities on LR interactions, indep


Keywords: Long-range, Topological superconductor, Quantum geometric Tensor, Non-Hermitian, Criticality