NUMERICAL CALCULATION OF THE COMPLEX BERRY PHASE IN NON-HERMITIAN SYSTEMS

Abstract

We numerically investigate topological phases of periodic lattice systems in tight-binding description under the influence of dissipation. The effects of dissipation are effectively described by <em>PT</em>-symmetric potentials. In this framework we develop a general numerical gauge smoothing procedure to calculate complex Berry phases from the biorthogonal basis of the system's non-Hermitian Hamiltonian. Further, we apply this method to a one-dimensional <em>PT</em>-symmetric lattice system and verify our numerical results by an analytical calculation.