Non-Hermitian quantum impurity systems in and out of equilibrium: noninteracting case

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.

Non-Hermitian Physics

“…From a broader perspective, a non-Hermitian TLL has also been discussed by Affleck et al [654] in the context of vortex pinnings originally discussed by Hatano and Nelson for a singleparticle lattice model [71]. The analogous winding RG flows have also been discussed in the non-Hermitian Kondo models [649,655,656] (Fig. 28(d)), where the Bethe-ansatz techniques have been found to remain useful.…”

Activity-induced phase transition in a quantum many-body system

“…Part of the reason is that the corresponding quantum system must be open (i.e., non-Hermitian), which is typically more difficult to control both in experiment and theory compared with closed (i.e., Hermitian) systems. In recent years, however, there is rapidly growing interest in studying non-Hermitian quantum systems [13,14] due to the advances in atomic-molecular-optical experiments allowing control over open quantum systems [15,16] and theoretical developments exploring quantum critical phenomena [17][18][19][20][21] and topological phases [22][23][24][25][26][27][28]. We are therefore in position to ask whether there exist new phases of matter induced by activity (i.e., non-Hermitian terms that can be interpreted as self-driving) in quantum many-body systems, and if so, how they can be realized in experiments.…”