2024/12/07 by Hu, Mengying, Lin, Jing, Ding, Kun
#Classical Physics (physics.class-ph) #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2412.05607
The hyperbolic lattice (HBL) has emerged as a compelling platform for exploring matter in non-Euclidean space. Among its notable features, the breakdown of the conventional Bloch theorem stands out, prompting a reexamination of band theory, with the determination of spectra for non-Hermitian systems being a prominent example. Here, we develop an approach to determining the spectra under open boundary conditions (OBCs), one of the foundations in non-Hermitian lattices, from the reciprocal space of HBLs. By introducing supercells to encompass states that are allowed by non-Abelian translational groups, we perform analytic continuation and base on the point gap topology to acquire uniform spectra, the universal OBC spectral range. Applying this method to a single-band nonreciprocal model and a reciprocal non-Abelian semimetal model, we reveal higher-dimensional skin effects and topological phase transitions, respectively, demonstrating the feasibility of our method in predicting spectral topology and investigating non-Hermitian physics in HBLs.