  In a class of non-Hermitian quantum walk in lossy lattices with open boundary
conditions, an unexpected peak in the distribution of the decay probabilities
appears at the edge, dubbed edge burst. It is proposed that the edge burst is
originated jointly from the non-Hermitian skin effect (NHSE) and the imaginary
gaplessness of the spectrum [Wen-Tan Xue et al., Phys. Rev. Lett. 128, 120401
(2022)]. Using a particular one-dimensional lossy lattice with a nonuniform
loss rate, we show that the edge burst can occur even in the absence of skin
localization. Furthermore, we discuss that the edge burst may not appear if the
spectrum satisfies the imaginary gaplesness condition. Aside from its
fundamental importance, by removing the restrictions on observing the edge
burst effect, our results open the door to broader design space for future
applications of the edge burst effect.
