R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum

We analyze a correlated system in equilibrium with special emphasis on non-Hermitian topology inducing a skin effect. The pseudo-spectrum, computed by the real-space dynamical mean-field theory, elucidates that additional pseudo-eigenstates emerge for the open boundary condition in contrast to the dependence of the density of states on the boundary condition. We further discuss how the line-gap topology, another type of non-Hermitian topology, affects the pseudo-spectrum. Our numerical simulation clarifies that while the damping of the quasi-particles induces the non-trivial point-gap topology, it destroys the non-trivial line-gap topology. The above two effects are also reflected in the temperature dependence of the local pseudo-spectral weight.