Non-Hermitian physics in open quantum many-body systems provides novel opportunities for the discovery of exotic quantum phenomena unexpected in Hermitian systems. A previous study of the non-Hermitian Kondo problem in ultracold atoms reports reversion of renormalization group flows which violates the $g$ theorem and produces an unusual quantum phase transition. In this work, we study the effect of electron-electron interactions by considering the non-Hermitian Kondo problem in a Luttinger liquid. By performing a perturbative renormalization group analysis to two-loop order, we find that the interplay between non-Hermitian Kondo couplings and electron-electron interactions can produce a pair of complex fixed points. Complex fixed points have often been discussed in an attempt to understand the extremely long correlation length of Hermitian systems with weakly first-order transitions. Here, we show that complex fixed points arise naturally and can be physically realized in open quantum systems. We discuss consequences of the complex fixed points and future directions.
Bosonization solution of the Kondo lattice in a Luttinger liquid
Universidad Nacional de La Plata（拉普拉塔国立大学）；University of Cincinnati（辛辛那提大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；Instituto de Física de La Plata - CONICET（拉普拉塔物理研究所-阿根廷国家科学研究委员会）
We show how Oshikawa's theorem for the Fermi surface volume of the Kondo lattice can be extended to the SU$(N)$ symmetric case. By extending the theorem, we are able to show that the mechanism of Fermi surface expansion seen in the large $N$ mean-field theory is directly linked to the expansion of the Fermi surface in a spin-$1/2$ Kondo lattice. This linkage enables us to interpret the expansion of the Fermi surface in a Kondo lattice as a fractionalization of the local moments into heavy electrons. Our method allows extension to a pure U(1) spin liquid, where we find the volume of the spinon …
We study the non-equilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL, the domain wall develops into a flat central region that spreads out ballistically faster than the conventional Lieb-Robinson maximal speed. By evaluating the current inside the regular lightcone, we find a universal conductance $e^2/h$, insensitive to the strength of the PT-symmetric interaction. On the other hand, by repeating the very same time evolution …
Correlated materials have appeared as an arena to study non-Hermitian effects as typically exemplified by the emergence of exceptional points. We show here that topological Kondo insulators are an ideal platform for studying these phenomena due to strong correlations and surface states exhibiting a nontrivial spin texture. Using numerical simulations, we demonstrate the emergence of exceptional points in the single-particle Green's function on the surface of the material while the bulk is still insulating. We reveal how quasiparticle states with long lifetimes are created on the surface by non…
Non-Hermitian Numerical Renormalization Group: Solution of the non-Hermitian Kondo model
School of Physics, University College Dublin（都柏林大学学院物理学院）；Centre for Quantum Engineering, Science, and Technology, University College Dublin（都柏林大学学院量子工程、科学与技术中心）
We study a system consisting of a Luttinger liquid coupled to a quantum dot on the boundary. The Luttinger liquid is expressed in terms of fermions interacting via density-density coupling and the dot is modeled as an interacting resonant level on to which the bulk fermions can tunnel. We solve the Hamiltonian exactly and construct all eigenstates. We study both the zero and finite temperature properties of the system, in particular we compute the exact dot occupation as a function of the dot energy in all parameter regimes. The system is seen to flow from weak to to strong coupling for all va…
We study the real-time dynamics of the Kondo effect after a quantum quench in which a magnetic impurity is coupled to two metallic Hubbard chains. Using an effective field theory approach, we find that for noninteracting electrons the charge current across the impurity is given by a scaling function that involves the Kondo time. In the interacting case, we show that the Kondo time decreases with the strength of the repulsive interaction and the time dependence of the current reveals signatures of the Kondo effect in a Luttinger liquid. In addition, we verify that the relaxation of the impurity…
The non-interacting and non-Hermitian, parity-time ($\mathcal{PT}$)-symmetric Anderson model exhibits an exceptional point (EP) at a non-Hermitian coupling $g=1$, which remains unrenormalized in the presence of interactions (Lourenco et al, arXiv:1806.03116), where the EP was shown to coincide with the quantum critical point (QCP) for Kondo destruction. In this work, we consider a quantum dot hybridizing with metallic leads having Rashba spin-orbit coupling ($λ$). We show that for a non-Hermitian hybridization, $λ$ can renormalize the exceptional point even in the non-interacting case, stabili…
