We investigate the Kondo effect in an open quantum system, motivated by recent experiments with ultracold alkaline-earth(-like) atoms. Because of inelastic collisions and the associated atom losses, this system is described by a complex-valued Kondo interaction and provides a non-Hermitian extension of the Kondo problem. We show that the non-Hermiticity induces anomalous reversion of renormalization-group flows which violate the g theorem due to nonunitarity and produce a quantum phase transition unique to non-Hermiticity. Furthermore, we exactly solve the non-Hermitian Kondo Hamiltonian using a generalized Bethe ansatz method and find the critical line consistent with the renormalization-group flow.
We investigate the Kondo effect in an open quantum system, motivated by recent experiments with ultracold alkaline-earth(-like) atoms. Because of inelastic collisions and the associated atom losses, this system is described by a complex-valued Kondo interaction and provides a non-Hermitian extension of the Kondo problem. We show that the non-Hermiticity induces anomalous reversion of renormalization-group flows which violate the g theorem due to nonunitarity and produce a quantum phase transition unique to non-Hermiticity. Furthermore, we exactly solve the non-Hermitian Kondo Hamiltonian using a generalized Bethe ansatz method and find the critical line consistent with the renormalization-group flow.
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.
Non-Hermitian (NH) Hamiltonians describe open quantum systems, nonequilibrium dynamics, and dissipative processes. Although a rich range of single-particle NH physics has been uncovered, many-body phenomena in strongly correlated NH systems have been far less well studied. The Kondo effect, an important paradigm for strong correlation physics, has recently been considered in the NH setting. Here, we develop an NH generalization of the numerical renormalization group and use it to solve the NH Kondo model. Our nonperturbative solution applies beyond weak coupling, and we uncover a nontrivial phase diagram. The method is showcased by application to the NH pseudogap Kondo model, which we show supports a completely novel phase with a genuine NH stable fixed point and complex eigenspectrum. Our NH numerical renormalization group code, which can be used in regimes and for models inaccessible to, e.g., perturbative scaling and Bethe ansatz, is provided open source.
Non-Hermitian Hamiltonians, as effective models, capture phenomena such as energy dissipation and nonunitary evolution in open quantum systems. New phases and phenomena appear that are not present in their Hermitian counterparts. Such a Hamiltonian, the non-Hermitian Kondo model, has been used to describe inelastic scattering between mobile and confined atoms in an optical lattice [M. Nakagawa, N. Kawakami, and M. Ueda, Phys. Rev. Lett. 121, 203001 (2018)]. Using a combination of Bethe ansatz and perturbative calculation, the authors argued that this model has two distinct phases: the Kondo and the non-Kondo phases, where the impurity is screened and unscreened, respectively. We show, however, that a novel phase termed $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{YSR}$ emerges between the Kondo and unscreened phases. Characterized by two RG invariants: a generalized Kondo temperature (TK) and a loss strength parameter ($\ensuremath{\alpha}$), the system exhibits three distinct phases. In the increasing order of losses, they are: the Kondo phase ($0<\ensuremath{\alpha}<\ensuremath{\pi}/2$), the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{YSR}$ phase ($\ensuremath{\pi}/2<\ensuremath{\alpha}<3\ensuremath{\pi}/2$), and the local moment phase ($\ensuremath{\alpha}>3\ensuremath{\pi}/2$). Notably, phase transition driven by dissipation occurs across $\ensuremath{\alpha}=\ensuremath{\pi}/2$, where both energetics and different timescales associated with loss play roles.
Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of nondiagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.
We demonstrate that laser excitations can coherently induce a novel Kondo effect in ultracold atoms in optical lattices. Using a model of alkaline-earth fermions with two orbitals, it is shown that the optically coupled two internal states are dynamically entangled to form the Kondo-singlet state, overcoming the heating effect due to the irradiation. Furthermore, a lack of SU(N) symmetry in the optical coupling provides a peculiar feature in the Kondo effect, which results in spin-selective renormalization of effective masses. We also discuss the effects of interorbital exchange interactions, and reveal that they induce novel crossover or reentrant behavior of the Kondo effect owing to control of the coupling anisotropy. The laser-induced Kondo effect is highly controllable by tuning the laser strength and the frequency, and thus offers a versatile platform to study the Kondo physics using ultracold atoms.
Non-Hermiticity plays a fundamental role in open quantum systems and describes a wide variety of effects of interactions with environments, including quantum measurement. However, understanding its consequences in strongly interacting systems is still elusive due to the interplay between non-perturbative strong correlations and non-Hermiticity. While the Wilsonian renormalization group (RG) method has been applied to tackle this problem, its foundation, based on the existence of the partition function, is ill-defined. In this paper, we establish a microscopic foundation of the non-Hermitian RG method from a few-body perspective. We show that the invariance of the scattering amplitude under RG transformations enables us to rigorously derive the non-Hermitian RG equation, giving a physically transparent interpretation of RG flows. We discuss a detailed structure of such RG flows in a non-relativistic two-body system with inelastic two-body loss, and show its relation to a non-Hermitian quantum scale anomaly. Our analysis suggests that non-Hermitian complex potentials often used in high-energy physics can be interpreted as being caused by quantum measurement, where the detection of elastically scattered particles updates the observer's knowledge, resulting in a nonunitary state change of the system. We apply our formalism to nuclear physics, find the emergence of a critical semicircle, and show that several nuclei are located near the critical semicircle in the coherent neutron-nucleus scattering. We also propose that the localized dineutron in two-neutron halo nuclei can be interpreted as the quantum measurement effect on the imaginary potential associated with absorption into the core nucleus. Our result bridges different contexts of non-Hermitian systems in high-energy and atomic, molecular, and optical physics, opening an interdisciplinary playground of non-Hermitian few-body physics.