Non-Hermitian Topological Magnonics

In the high analysis model, the hopping from left to right (tL) and from right to left (tR) differs from tI, making the Hamiltonian non-Hermitian. When tL is greater than tR, modes accumulate at the left edge of the chain. Conversely, when tR is greater than tL, modes accumulate at the right edge. This is a typical example demonstrating how the energy spectrum characterizes non-Hermitian topology, analyzed under periodic boundary conditions. Non-Hermitian effects are evident in the energy spectrum, with the real part on the X-axis and the imaginary part on the Y-axis. The non-Hermitian effect occurs when the spectra form a loop, and the evolution direction of the wave vector in the first Brillouin zone (clockwise or anti-clockwise) corresponds to accumulation at the left or right edge of the chain.