Fig. 2: Higher-dimensional skin effects.
From: Generalization of non-Hermitian spectral topology to hyperbolic lattices
Spectra (blue circles) of a a higher-dimensional Euclidean lattice (HDEL) and b the corresponding OBC configuration. Regions \({\sigma }_{{{\rm{P}}}}^{(1)}\) and \({\sigma }_{{{\rm{U}}}}^{(1)}\) are plotted in gray and red, respectively. Magenta asterisks in (a) are obtained by substituting quantized momenta into \({H}^{(1)}({{\boldsymbol{k}}})\). The values of \(\left\{{k}_{2},{k}_{3},{k}_{4}\right\}\) for the white and green lines in (a) are \(\left\{\pi /7,\pi /7,\pi /7\right\}\) and \(\left\{\pi /{\mathrm{4,2}}\pi /3,\pi /2\right\}\), respectively. All results in a are obtained under PBC settings. The histograms in b display the Kullback–Leibler (KL) divergence between the right and left eigenvectors for states within the range highlighted by the white arrow. Distribution of Green’s functions (blue circles in top panels) and spectral sums of eigenstates (red spheres in bottom panels) along c \({\gamma }_{1}\) and d \({\gamma }_{2}\) directions, with marker sizes proportional to their magnitudes. The numbers denote the source and probe positions. Excitation energy is \(E=2.5\). The HDEL contains 1296 sites with explicit geometry defined in the second paragraph of the “Higher-dimensional skin effects” subsection of the main text.
