Level statistics of extended states in random non-Hermitian Hamiltonians
C. Wang, X. R. Wang
Abstract
Absence of quasiparticle-level anticrossing in random non-Hermitian systems is demonstrated. As a result, the general Wigner-Dyson distributions of energy-level spacing of diffusive metals in the usual Hermitian systems is replaced by the Poisson distribution for quasiparticle-level (the real parts of complex eigenenergies) spacing of non-Hermitian disordered metals in the thermodynamic limit of infinite system size. This is a very surprising result because Poisson statistics is universally true for the Anderson insulators where energy eigenstates do not overlap with each other, so energy levels are independent from each other. For disordered metals where different eigenstates overlap with each other, one should expect different levels trying to stay away from each other, so the Poisson distribution should not apply there. Our results show that the larger non-Hermitian energy (dissipation) can invalidate the quasiparticle-level anticrossing that holds dearly in Hermitian metals. Thus, our theory provides a unified picture for recently discovered ``level attraction'' in various systems, as well as a theoretical basis for manipulating quasiparticle energy levels.