  Non-Hermitian phenomena offer a novel approach to analyze and interpret
spectra in the presence of interactions. Using the density-matrix
renormalization group (DMRG), we demonstrate the existence of exceptional
points for the one-particle Green's function of the 1D alternating Hubbard
chain with chiral symmetry, with a corresponding Fermi arc at zero frequency in
the spectrum. They result from the non-Hermiticity of the effective Hamiltonian
describing the Green's function and only appear at finite temperature. They are
robust and can be topologically characterized by the zeroth Chern number. This
effect illustrates a case where temperature has a strong effect in 1D beyond
the simple broadening of spectral features. Finally, we demonstrate that
exceptional points appear even in the two-particle Green's function (charge
structure factor) where an effective Hamiltonian is difficult to establish, but
move away from zero frequency due to a distinct symmetry constraint.
