Non-Hermitian quantum impurity systems in and out of equilibrium: Noninteracting case
Takato Yoshimura, Kemal Bidzhiev, Hubert Saleur
Abstract
We provide systematic analysis on a non-Hermitian $\mathcal{PT}$-symmetric quantum impurity system both in and out of equilibrium, based on exact computations. In order to understand the interplay between non-Hermiticity and Kondo physics, we focus on a prototypical noninteracting impurity system, the resonant level model, with complex coupling constants. Explicitly constructing biorthogonal basis, we study its thermodynamic properties as well as the Loschmidt echo starting from the initially disconnected two free fermion chains. Remarkably, we observe the universal crossover physics in the Loschmidt echo, both in the $\mathcal{PT}$ broken and unbroken regimes. We also find that the ground state quantities we compute in the $\mathcal{PT}$ broken regime can be obtained by analytic continuation. It turns out that Kondo screening ceases to exist in the $\mathcal{PT}$ broken regime, which was also previously predicted in the non-Hermitian Kondo model. All the analytical results are corroborated against biorthogonal free fermion numerics.