Exceptional points in the one-dimensional Hubbard model

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.

Automated summary

The paper presents a new method of analyzing and interpreting spectra in the presence of interactions using non-Hermitian phenomena. By utilizing the density-matrix renormalization group, the existence of exceptional points in the one-dimensional Hubbard chain with chiral symmetry is demonstrated, showing a Fermi arc at zero frequency in the spectrum. These points are a result of the non-Hermiticity of the effective Hamiltonian and are only present at finite temperature.