Exceptional points in the one-dimensional Hubbard model

TL;DR

This paper reveals the existence of exceptional points in the one-dimensional Hubbard model's Green's function at finite temperature, highlighting their topological nature and impact on spectral features, with implications for non-Hermitian physics in correlated systems.

Contribution

It demonstrates the presence of exceptional points in the 1D Hubbard model's Green's functions using DMRG, revealing their topological characterization and temperature dependence, a novel insight in strongly correlated systems.

Findings

Exceptional points exist in the one-particle Green's function at finite temperature.

These points are topologically characterized by the zeroth Chern number.

Exceptional points also appear in the two-particle Green's function, influenced by symmetry constraints.

Abstract

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.