  In quantum materials, basic observables such as spectral functions and
susceptibilities are determined by Green's functions and their complex
quasiparticle spectrum rather than by bare electrons. Even in closed many-body
systems, this makes a description in terms of effective non-Hermitian (NH)
Bloch Hamiltonians natural and intuitive. Here, we discuss how the abundance
and stability of nodal phases is drastically affected by NH topology. While
previous work has mostly considered complex degeneracies known as exceptional
points as the NH counterpart of nodal points, we propose to relax this
assumption by only requiring a crossing of the real part of the complex
quasiparticle spectra, which entails a band crossing in the spectral function,
i.e. a nodal spectral function. Interestingly, such real crossings are
topologically protected by the braiding properties of the complex Bloch bands,
and thus generically occur already in one-dimensional systems without symmetry
or fine-tuning. We propose and study a microscopic lattice model in which a
sublattice-dependent interaction stabilizes nodal spectral functions. Besides
the gapless spectrum, we identify non-reciprocal charge transport properties
after a local potential quench as a key signature of non-trivial band braiding.
Finally, in the limit of zero interaction on one of the sublattices, we find a
perfectly ballistic unidirectional mode in a non-integrable environment,
reminiscent of a chiral edge state known from quantum Hall phases. Our analysis
is corroborated by numerical simulations both in the framework of exact
diagonalization and within the conserving second Born approximation.
