Probing non-Hermitian skin effect and non-Bloch phase transitions

In non-Hermitian crystals showing the non-Hermitian skin effect, ordinary\nBloch band theory and Bloch topological invariants fail to correctly predict\nenergy spectra, topological boundary states, and symmetry breaking phase\ntransitions in systems with open boundaries. Recently, it has been shown that a\ncorrect description requires to extend Bloch band theory into complex plane. A\nstill open question is whether non-Hermitian skin effect and non-Bloch\nsymmetry-breaking phase transitions can be probed by real-space wave dynamics\nfar from edges, which is entirely governed by ordinary Bloch bands. Here it is\nshown that the Lyapunov exponent in the long-time behavior of bulk wave\ndynamics can reveal rather generally non-Bloch symmetry breaking phase\ntransitions and the existence of the non-Hermitian skin effect.\n