Fig. 5: Egienspectrum and number density imbalance beyond half-filling.

a Eigenvalue spectrum and (b) the number density imbalance in the Hatano-Nelson model of spin-half fermions under both open and periodic boundary conditions when total number of fermions N = 7 is one smaller than the lattice size L = 8. The green squares and purple circles refer to the results for periodic and open boundary conditions, respectively. The imbalance \({{{{{{\mathcal{I}}}}}}}_{E}^{R}\) is calculated by Eq. (5). All results are obtained when the ratio of Coulomb repulsion U to hopping strength t (U/t) is 10 and the imaginary vector potential A is 0.3.