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

• Received 27 June 2019
• Revised 15 August 2019

DOI:https://doi.org/10.1103/PhysRevResearch.1.023013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society