Abstract
We provide systematic analysis on a non-Hermitian 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 PT broken and unbroken regimes. We also find that the ground state quantities we compute in the PT broken regime can be obtained by analytic continuation. It turns out that Kondo screening ceases to exist in the 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.
Highlights
Quantum impurity systems, such as the Kondo model, serve as representative examples where nonperturbative quantum many-body effects give rise to unconventional low-temperature behaviours that are in stark contrast with those of Fermi liquids [1]
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
The KT renormalization group (RG) flow is relevant to the(anisotropic) Kondo model, and the circular behavior was explored in this context in [11], where it was concluded that the Kondo effect might disappear in the non-hermitian case
Summary
Quantum impurity systems, such as the Kondo model, serve as representative examples where nonperturbative quantum many-body effects give rise to unconventional low-temperature behaviours that are in stark contrast with those of Fermi liquids [1]. This is partly motivated by set-ups such as the one in [10], where a non-Hermitian Kondo model is obtained as an effective model that characterizes ultra-cold mobile and immobile atoms that undergo inelastic scatterings (resulting in two-body losses) Another motivation comes from the old observation [12,13,14] that making the couplings complex in the Kosterlitz-Thouless (KT) renormalization group (RG) flow can profoundly change the low-energy physics, and lead sometimes to “circular” behavior. In the Hermitian case, a great deal of the physics of quantum impurity problems both in and out of equilibrium can be learned without the Bethe-ansatz, by studying the resonant level model (RLM) [16], which occurs as a simpler (Toulouse) limit of interacting impurity systems such as the anisotropic Kondo model and the interacting resonant level model It is natural, in order to clarify what happens to quantum-impurity problems in the non-Hermitian case, to start by studying a PT -symmetric version of the RLM (PTRLM) model. The impurity couples to the leads with hopping amplitudes γ and γ∗ (or tunneling strength)
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