Exceptional points in the one-dimensional Hubbard model

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 Greens 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 Greens 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 Greens function (charge structure factor) where an effective Hamiltonian is difficult to establish, but move away from zero frequency due to a distinct symmetry constraint.

Real-space dynamical mean field theory study of non-Hermitian skin effect for correlated systems: Analysis based on pseudospectrum

“…As well as the above dissipative systems, the non-Hermitian topology also provides a novel perspective of strongly correlated systems in equilibrium 65,66 . In such a system, the single-particle spectrum is described by an effective non-Hermitian Hamiltonian which is composed of the non-interacting Hamiltonian and the selfenergy 21,27,[65][66][67][68][69][70][71][72][73][74][75] . So far, it has been elucidated that exceptional points induce the bulk Fermi arc in the singleparticle spectrum for equilibrium correlated systems.…”

Machine Learning of Mirror Skin Effects in the Presence of Disorder

“…Among them, non-Hermitian topology attracts much attention in these years . The platforms of non-Hermitian topological physics extends to a wide variety of systems such as, open quantum systems [12-15, 30, 48], electric circuits [17,21,22,49,50], photonic crystals [6,16,18,19,[51][52][53][54][55], equilibrium system of quasiparticles [46,[56][57][58][59][60][61][62][63][64], and so on.…”