Multichannel Kondo Model Research Articles

Dynamic mass generation and topological order in overscreened Kondo lattices

Multichannel Kondo lattice models are examples of strongly correlated electronic systems that exhibit non-Fermi-liquid behavior due to the presence of a continuous channel symmetry. Mean-field analyses have predicted that these systems undergo channel symmetry breaking at low temperature. We use the dynamical large-N technique to study temporal and spatial fluctuations of the multichannel Kondo model on a honeycomb lattice and find that this prediction is not generally true. Rather, we find a (2+1)-dimensional conformally invariant fixed point, governed by critical exponents that are found numerically. When we break time-reversal symmetry by adding a Haldane mass to the conduction electrons, three phases, separated by continuous transitions, are discernible: one characterized by dynamic mass generation and spontaneous breaking of the channel symmetry, one where topological defects restore channel symmetry but preserve the gap, and one with a Kondo-coupled chiral spin liquid. We argue that the last phase is a fractional Chern insulator with anyonic excitations. Published by the American Physical Society 2024

Frustration shapes multi-channel Kondo physics: a star graph perspective

We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalisation group technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids (NFLs). The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature. Despite the absence of inter-channel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them. A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local NFLs arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signalling the underlying orthogonality catastrophe associated with the degenerate ground state manifold. We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling.

Manipulating Non-Abelian Anyons in a Chiral Multichannel Kondo Model

Non-Abelian anyons are fractional excitations of gapped topological models believed to describe certain topological superconductors or quantum Hall states. Here, we provide the first numerical evidence that they emerge as independent entities also in gapless electronic models. Starting from a multi-impurity multichannel chiral Kondo model, we introduce a novel mapping to a single-impurity model, amenable to Wilson's numerical renormalization group. We extract its spectral degeneracy structure and fractional entropy, and calculate the F matrices, which encode the topological information regarding braiding of anyons, directly from impurity spin-spin correlations. Impressive recent advances on realizing multichannel Kondo systems with chiral edges may thus bring anyons into reality sooner than expected.

Multi-impurity chiral Kondo model: Correlation functions and anyon fusion rules

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the interimpurity spin correlation probes the anyon fusion of the pair of correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid the multichannel Kondo anyons via consecutive measurements.

Order parameter for the multichannel Kondo model at quantum criticality

A multichannel Kondo model, where two or more equivalent but independent channels of electrons compete to screen a spin-1/2 impurity, shows overcompensation of the impurity spin, leading to the non-Fermi-liquid behavior in various thermodynamic and transport properties. However, when the channel symmetry is broken, an impurity quantum phase transition can occur at zero temperature. Identification of an order parameter describing the impurity quantum phase transition is very difficult since it is beyond the conventional Landau-Ginzburg-Wilson theory. By employing the natural orbitals renormalization group method, we study both two-channel and threechannel Kondo models, from the perspective of spin correlation between the impurity and electrons in electronic channels. Here we demonstrate that by introducing the spin-correlation ratio as an order parameter we can characterize impurity quantum phase transitions driven by channel asymmetry. In particular, the universal critical exponents $\beta$ of the spin-correlation ratio and $\nu$ of the correlation length are explicitly determined by finite-sizescaling analysis, namely, $\beta = 0.10(1), \nu = 2.0(1)$, and $\beta = 0.10(1), \nu = 2.5(1)$ for the two-channel and three-channel Kondo models, respectively.

Quantum Coherence and the Kondo Effect in the 2D Electron Gas of Magnetically Undoped AlGaN/GaN High-Electron-Mobility Transistor Heterostructures

The unusual observation of the Kondo effect in the two-dimensional electron gas (2DEG) of magnetically undoped AlGaN/GaN heterostructures is reported. The temperature-dependent zero-field resistivity data exhibits an upturn below 120 K, while the standard low-temperature weak localization and then weak antilocalization behaviour is revealed at T → 0. Magnetic transport investigations of the system are performed in the temperature range of 0.1–300 K and at magnetic fields up to 8 T, applied perpendicularly to the 2DEG plane. The experimental data are analyzed in terms of the multichannel Kondo model for d0 magnetic materials and weak localization theory taking into account the spin-orbit interaction.

Квантовая когерентность и эффект Кондо в двумерном электронном газе магнитно-нелегированных гетероструктур AlGaN/GaN

Abstract The unusual observation of the Kondo effect in the two-dimensional electron gas (2DEG) of magnetically undoped AlGaN/GaN heterostructures is reported. The temperature-dependent zero-field resistivity data exhibits an upturn below 120 K, while the standard low-temperature weak localization and then weak antilocalization behaviour is revealed at T → 0. Magnetic transport investigations of the system are performed in the temperature range of 0.1–300 K and at magnetic fields up to 8 T, applied perpendicularly to the 2DEG plane. The experimental data are analyzed in terms of the multichannel Kondo model for d _0 magnetic materials and weak localization theory taking into account the spin-orbit interaction.

The Kondo effect in 2D electron gas of magnetically undoped AlGaN/GaN high-electron-mobility transistor heterostructures

Unusual observation of the Kondo effect in two-dimensional electron gas (2DEG) of magnetically undoped AlGaN/GaN high-electron-mobility transistor heterostructures is reported. The temperature-dependent zero-field resistivity data exhibited an upturn below 120 K, while the standard low-temperature weak-localization behaviour was revealed at T → 0. Magnetotransport characterization was carried out in the magnetic fields up to 80 kOe, applied perpendicular to the 2DEG plane, in the temperature range 1.8 ÷ 300 K. Negative low-temperature magnetoresistance with a magnitude of order of 1 % was detected. The data set is analysed in the frame of the multichannel Kondo model for d0-magnetic materials.

Kondo effect due to a hydrogen impurity in graphene: A multichannel Kondo problem with diverging hybridization

We consider the Kondo effect arising from a hydrogen impurity in graphene. As a first approximation, the strong covalent bond to a carbon atom removes that carbon atom without breaking the $C_{3}$ rotation symmetry, and we only retain the Hubbard interaction on the three nearest neighbors of the removed carbon atom which then behave as magnetic impurities. These three impurity spins are coupled to three conduction channels with definite helicity, two of which support a diverging local density of states (LDOS) $\propto 1/ [ | \omega \ | \ln ^{2}( \Lambda /| \omega \ | \ ) \ ] $ near the Dirac point $\omega \rightarrow 0$ even though the bulk density of states vanishes linearly. We study the resulting 3-impurity multi-channel Kondo model using the numerical renormalization group method. For weak potential scattering, the ground state of the Kondo model is a particle-hole symmetric spin-$1/2$ doublet, with ferromagnetic coupling between the three impurity spins; for moderate potential scattering, the ground state becomes a particle-hole asymmetric spin singlet, with antiferromagnetic coupling between the three impurity spins. This behavior is inherited by the Anderson model containing the hydrogen impurity and all four carbon atoms in its vicinity.

Many-terminal Majorana island: From topological to multichannel Kondo model

We study Kondo screening obtained by coupling Majorana bound states, located on a topological superconducting island, to interacting electronic reservoirs. At the charge degeneracy points of the island, we formulate an exact mapping onto the spin-$1/2$ multi-channel Kondo effect. The coupling to Majorana fermions transforms the tunneling terms into effective fermionic bilinear contributions with a Luttinger parameter $K$ in the leads that is effectively doubled. For strong interaction, $K=1/2$, the intermediate fixed point of the standard multi-channel Kondo model is exactly recovered. It evolves with $K$ and connects to strong coupling in non-interacting case $K=1$, with maximum conductance between the leads and robustness against channel asymmetries similarly to the topological Kondo effect. For a number of leads above four, there exists a window of Luttinger parameters in which a quantum phase transition can occur between the strong coupling topological Kondo state and the partially conducting multi-channel Kondo state.

Possible realization of a multichannel Kondo model in a system of magnetic chains

We discuss a possible realization of overscreened multi-channel Kondo model in quasi-one-dimensional magnets.

Large rank Wilson loops in $ \mathcal{N} = 2 $ superconformal QCD at strong coupling

We compute the expectation values of circular Wilson loops in large representations at strong coupling, in the large-N limit of the N=2 superconformal theory with SU(N) gauge group and 2N hypermultiplets. Employing Pestun's matrix integral, we focus attention on symmetric and antisymmetric representations with ranks of order N. We find that large rank antisymmetric loops are independent of the coupling at strong 't Hooft coupling while symmetric Wilson loops grow exponentially with it. Symmetric loops display a non-analyticity as a function of the rank, characterized by the splitting of a single matrix model eigenvalue from the continuum, bearing close resemblance to Bose-Einstein condensation in an ideal gas. We discuss implications of these for a putative large-N string dual. The method of calculation we adopt makes explicit the connection to Fermi and Bose gas descriptions and also suggests a tantalizing connection of the above system to a multichannel Kondo model.

Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots

In this paper, we study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We assume the dot is small enough that its level spacing is large compared to both the temperature and the coupling to the spatially proximate bulk non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level is governed by a $k$-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction $\ensuremath{\nu}=2+k/(k+2)$ or its particle-hole conjugate at $\ensuremath{\nu}=2+2/(k+2)$. The $k$-channel Kondo model is channel symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi-liquid and Fermi-liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of $k=2$, our results provide a distinct venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction $\ensuremath{\nu}=5/2$. We present numerical estimates for realizing this scenario in experiment.

Quantum oscillations in the underdoped cuprate

Quantum oscillations occur via Landau quantisation of the quasiparticle in a Fermi liquid at low temperature. In the light of currently popular notions their detection in the ortho-II-YBa 2Cu 3O 6.45 and YBa 2Cu 4O 8 crystals is inconsistent with this. We explain this in terms of multichannel Kondo model of the underdoped cuprate.

Exact scaling functions of the multichannel Kondo model

We reinvestigate the large degeneracy solution of the multichannel Kondo problem, and show how in the universal regime the complicated integral equations simplifying the problem can be mapped onto a first order differential equation. This leads to an explicit expression for the full zero-temperature scaling functions at - and away from - the intermediate non Fermi Liquid fixed point, providing complete analytic information on the universal low - and intermediate - energy properties of the model. These results also apply to the widely-used Non Crossing Approximation of the Anderson model, taken in the Kondo regime. An extension of this formalism for studying finite temperature effects is also proposed and offers a simple approach to solve models of strongly correlated electrons with relevance to the physics of heavy fermion compounds.

A Kondo-like thermoelectric power behaviour of UAsSe ferromagnet

We have investigated thermoelectric power of some uranium arsenochalcogenides (UAsS and UAs1−xSe1+x) and dipnictides (UP2, UP1.7As0.3 and UAs2) that crystallise in tetragonal structure and order ferro- and antiferro-magnetically, respectively. The thermoelectric power, S(T), is strongly anisotropic for all examined systems. While S(T) along c-axis displays a complex behaviour for all the compounds, a broad peak of S(T) along a-axis around 60K has been observed only for the arsenochalcogenides. We ascribe it to be of a Kondo origin. A dependence of the peak behaviour on x is discussed in the frame of the multi-channel Kondo model.

Quantum critical points of an anisotropic multichannel Kondo impurity

The low-temperature behavior of a magnetic impurity of spin S interacting with an electron gas via an anisotropic spin exchange is studied via Bethe’s ansatz. The multichannel Kondo model with U(1) invariance is integrable as a function of two continuous (the exchange and the anisotropy) and two discrete parameters, namely the impurity spin S and the number of channels n. As a function of S and n we distinguish: (i) the compensated case with n=2S, (ii) the overcompensated case if n>2S, and (iii) the undercompensated case (n<2S). While in case (i) the ground state is a singlet, the cases (ii), and (iii) yield quantum critical points. The undercompensated one is of a new type with the critical exponents depending on the anisotropy.

Dynamically induced multichannel Kondo effect

We study how the multichannel Kondo effect is dynamically induced to affect the photoemission and the inverse photoemission spectrum when an electron is emitted from (or added to) the completely screened Kondo impurity with spin $S>1/2.$ The spectrum thereby shows a power-law edge singularity characteristic of the multichannel Kondo model. We discuss this anomalous behavior by using the exact solution of the multichannel Kondo model and boundary conformal field theory. The idea is further applied to the photoemission for quantum spin systems, in which the edge singularity is controlled by the dynamically induced overscreening effect with a mobile Kondo impurity.

Residue Entropy of Overscreen Multi-Channel Kondo Model: a Study of Large K Expansion

We study the residue entropy of overscreen multi-channel Kondo model by means of perturbathe renormalization group. In this field theory framework one must use pseudofermion representation for local spin operator, and the constraint of pseudofermion must be treated properly. We treat the constraint by a method developed recently. In this method the partition function of the Kondo model is separated into proper weighted partition functions of subsystems. We study the overscreen multi-channel Kondo model through M-subsystem. From calculating the residue entropy of M-subsystem, we obtain the residue entropy of original system which agrees with the result of conformal field theory.

Spontaneous polarization of the Kondo problem associated with the higher-spin six-vertex model

We study the multi-channel Kondo model associated with an integrable higher-spin analogue of the anti-ferroelectric six-vertex model, which is constructed by inserting spin 1/2 to spin 1 lines: $... C^3 \otimes C^3 \otimes C^2 \otimes C^3 \otimes C^3 ... $. We formulate the problem in terms of representation theory of quantum affine algebra $U_q(hat{sl}_2)$. We derive an exact formula for the spontaneous staggered polarization for our model, which corresponds to Baxter`s formula for the six-vertex model.