Interplay between non-Fermi liquid and non-Hermiticity: A multi-method study of non-Hermitian multichannel Kondo model

Abstract

Non-Hermitian multichannel Kondo problems host both non-Fermi liquid and non-Hermitian physics, which provide a prototypical model to explore exotic collective quantum phenomena driven by the two different ingredients. Here, we first propose an experimental setup that realizes this model with exact channel symmetry as well as a controllable PT symmetry. Then, we perform a multi-method study of this model, focusing on the low-energy spectrum, the thermodynamic quantities, and the transport properties associated with different fixed points. Using the Bethe ansatz approach, we identify existence of the Yu-Shiba-Rusinov-like state previously found in the non-Hermitian single-channel Kondo model. Then, based on non-Hermitian numerical renormalization group calculations, we reveal clear numerical signatures of the Yu-Shiba-Rusinov state emerging in the relatively strong non-Hermiticity regime of the PT-asymmetric model. Furthermore, our boundary conformal field theory, which is found to be applicable for the PT-symmetric model, uncovers an anomalous temperature dependence of the Kondo conductance, which is beyond conventional Hermitian Kondo systems.

Figures (6)

• Figure 1: The schematic plot of the realization setup of the NHMCK model. (a) The multi-junction nanostructure, where the Majorana modes (the red dot) on a superconducting island are connected to normal leads. The tunneling between the Majorana mode and the lead is assisted by a quantum do (the orange dot). (b) A zoom-in plot of the Majorana-lead tunneling junction via the quantum dot. The quantum dot is further coupled to an environment. (c) The quantum dot has a single-body loss into the environment and monitored by a reservoir, and a post-selection is implemented on the Lindbladian dynamics of the quantum dot.
• Figure 2: Bethe ansatz calculations of multichannel non-Hermitian Kondo model without $\mathcal{PT}$ symmetry. The calculated spinon DOS contributed by the impurity for different $\alpha$ in the three phases, i.e., the Kondo phase, the bound-mode states in YSR-like phase, and the unscreened states (both YSR-like phase and unscreened phase). Similar results have been obtained for the single channel model in Ref. PhysRevB.111.L201106.
• Figure 3: The energy spectrum for the $\mathcal{PT}$-broken $n=2$ NHMCK model obtained by non-Hermitian NRG for different $\theta$. The upper ((a)(c)(e)) and lower ((b)(d)(f)) panel show the real and imaginary part, i.e., Re$(E)$ and Im$(E)$, respectively. The maximal absolute value of the imaginary parts are marked for each plot in (b)(d)(f). The first 50 eigenenergies are plot here. The black curves show the calculated Re$(E)$ corresponding to the Hermitian two-channel Kondo model with $\theta=0$.
• Figure 4: The nHNRG results of thermodynamic quantities as a function of temperature. (a) The calculated impurity entanglement entropy $S_{\rm imp}$ and impurity specific heat $C_{\rm imp}$ for the $\mathcal{PT}$-asymmetric $n=2$ NHMCK model. (b) The real and imaginary parts of the partition function $Z_N^{\rm LR}$ and (c) shows those of the impurity entropy $S_{\rm imp}$.
• Figure 5: The nHNRG results of the energy spectrum for the $\mathcal{PT}$-symmetric $n=2$ NHMCK model for different $\theta$.