Correction to Topological Properties of a Non-Hermitian Quasi-1D Chain with a Flat Band

C. Martínez-Strasser, M. A. J. Herrera, A. García-Etxarri, G. Palumbo, F. K. Kunst, D. Bercioux, Topological Properties of a Non-Hermitian Quasi-1D Chain with a Flat Band. Adv Quantum Technol. 2024, 7, 2300225.

In this correction to the article titled “Topological Properties of a Non-Hermitian Quasi-1D Chain with a Flat Band” we show that the previously claimed non-Hermitian skin effect found in the non-Hermitian diamond chain in configuration B (DCB) is mistaken. The observed accumulation of the eigenstates towards the edges in the representation used in Figure 5 results from an incorrect selection of the basis for the flat band eigenstates in the Wolfram Language (WL).

In general, states in the flat bands are defined as a linear combination of compact localized states (CLSs). However, the WL is unable to determine this basis. As a result, summing the squared amplitudes on each site leads to an accumulation that appears to increase in weight towards the boundaries (see Figure A(a)). Whereas a correct CLS base does not induce this accumulation - see Figure A(b).

As a result, Figure 5 and Figure 9 are incorrect. Replacement figures are shown in Figures B and D, respectively, below.

Additionally, Figure D shows the correct representation of the sum of amplitudes at each site of the rotated DCB model presenting real non-reciprocal couplings (refer to Figure 8b in the article). In this model, the right and left eigenvectors are identical. Notably, this model does not exhibit the non-Hermitian skin effect, neither on the sites producing the flat band nor on the Hermitian SSH chain coupled in a non-Hermitian fashion to the flat band sites (see Figure E).

The authors acknowledge useful discussions with Julius Gohsrich for giving insight to this matter.