Dissipation driven phase transition in the non-Hermitian Kondo model

Abstract

Non-Hermitian Hamiltonians capture several aspects of open quantum systems, such as dissipation of energy and non-unitary evolution. An example is an optical lattice where the inelastic scattering between the two orbital mobile atoms in their ground state and the atom in a metastable excited state trapped at a particular site and acting as an impurity, results in the two body losses. It was shown in \cite{nakagawa2018non} that this effect is captured by the non-Hermitian Kondo model. which was shown to exhibit two phases depending on the strength of losses. When the losses are weak, the system exhibits the Kondo phase and when the losses are stronger, the system was shown to exhibit the unscreened phase where the Kondo effect ceases to exist, and the impurity is left unscreened. We re-examined this model using the Bethe Ansatz and found that in addition to the above two phases, the system exhibits a novel $\widetilde{YSR}$ phase which is present between the Kondo and the unscreened phases. The model is characterized by two renormalization group invariants, a generalized Kondo temperature $T_K$ and a parameter `$\alpha$' that measures the strength of the loss. The Kondo phase occurs when the losses are weak which corresponds to $0<\alpha <\pi /2$. As $\alpha$ approaches $\pi /2$, the Kondo cloud shrinks resulting in the formation of a single particle bound state which screens the impurity in the ground state between $\pi /2<\alpha <\pi$. As $\alpha$ increases, the impurity is unscreened in the ground state but can be screened by the localized bound state for $\pi <\alpha <3\pi /2$. When $\alpha >3\pi /2$, one enters the unscreened phase where the impurity cannot be screened. We argue that in addition to the energetics, the system displays different time scales associated with the losses across $\alpha =\pi /2$, resulting in a phase transition driven by the dissipation in the system.

6 Pages, 2 Figures, 1 Appendix, due to the limitation "The abstract field cannot be longer than 1,920 characters", the abstract appearing here is slightly shorter than that in the PDF file. Small typo has been corrected in Eq. 2. Authors thank H. Saleur for pointing out the typo

References in corpus (17)

• Non-Hermitian Physics
• Light-induced gauge fields for ultracold atoms
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Acoustic non-Hermitian skin effect from twisted winding topology
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Localized magnetic moments with tunable spin exchange in a gas of ultracold fermions
• Observation of $\mathcal{P}\mathcal{T}$-symmetric quantum coherence in a single ion system
• Using Superconducting Qubit Circuits to Engineer Exotic Lattice Systems
• Observation of two-dimensional Anderson localisation of ultracold atoms
• $\mathcal{P}\mathcal{T}$-symmetric wave guide system with evidence of a third-order exceptional point
• Exploring the Kondo model in and out of equilibrium with alkaline-earth atoms
• Open quantum systems approach to atomtronics
• Construction of Fractal Order and Phase Transition with Rydberg Atoms
• Complex fixed points of the non-Hermitian Kondo model in a Luttinger liquid
• Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving $s$-wave one-dimensional superconductors
• Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain

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• Anderson Impurities In Edge States with Nonlinear and Dissipative Perturbations
• Nonequilibrium transport through an interacting monitored quantum dot
• Dissipative Kondo physics in the Anderson Impurity Model with two-body losses
• Interacting many-body non-Hermitian systems as Markov chains