Boundary Kondo Impurity with PT-symmetry and Beyond: a Bethe Ansatz approach

The development of cold atom experimental techniques and superconducting quantum computers allows the experimental study of dissipative 1D quantum many-body systems. These dissipative systems are often modeled by non-Hermitian Hamiltonians that typically arise when one wishes to provide an effective description of an open system coupled to an external environment.

This raises interesting questions about how these open systems differ from closed ones and what new physics would emerge in such systems. In this work, we study a one-dimensional conducting wire attached with complex coupling constants to Kondo impurities one at each edge, the two coupling constants being complex conjugates of each other leading to a PT-symmetric Hamiltonian. We also investigate how the physics changes when the PT symmetry is broken.

We solve the non-Hermitian Hamiltonian exactly with the Bethe Ansatz approach, obtain the spectrum of its eigenstates, and analyze their stability. We show that new phases arise, phases that do not exist in the conventional Kondo problem, and study boundary phase transitions between them.