Frustrated Kondo impurity triangle: A simple model of deconfinement

König, Elio J.; Coleman, Piers; Komijani, Yashar

doi:10.1103/physrevb.104.115103

Cited by 12 publications

(5 citation statements)

References 84 publications

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“…This prerequisite is generally not possible except for very rare cases [43][44][45][46][47][48][49], because the impurities often couple to the shared electron baths in different momentum-dependent form that cannot be easily disentangled. Therefore, many works assume models with independent baths and artificial exchange interactions between impurities, based on which various ground state phase diagrams have been predicted [34][35][36][37][38][39][40][41][42]50], but real systems often have shared baths that not only cause the Kondo screening but also mediate the RKKY interaction. This hinders wider applications of NRG.…”

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confidence: 99%

From Liverpool to Beijing and Chongqing: William Band’s Adventure in Wartime China

2019

Phys. Perspect.

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We propose an auxiliary-bath algorithm for the numerical renormalization group (NRG) method to solve multi-impurity models with shared electron baths. The method allows us to disentangle the electron baths into independent Wilson chains to perform standard NRG procedures beyond the widely adopted independent bath approximation. Its application to the 2-impurity model immediately reproduces the well-known even-and odd-parity channels. For 3-impurity Kondo models, we find successive screening of collective degrees of freedom such as the helicity and the cluster spin, and clarify the false prediction of a non-Fermi liquid ground state in unphysical parameter region in previous literature due to improper treatment of disentanglement. Our work highlights the importance of nonlocal spatial correlations due to shared baths and reveals a generic picture of successive collective screening for the entropy depletion that is crucial in real correlated systems. Our method greatly expands the applicability of the NRG and opens an avenue for its further development.

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confidence: 99%

From Liverpool to Beijing and Chongqing: William Band’s Adventure in Wartime China

2019

Phys. Perspect.

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“…The Kondo coupling J continues to flow under RG until it obtains a value dictated by the phase shift of the star graph: ρJ * = 2δ (l) /π = 2/K. Following equation (21), this also leads to the fractional value of 1/4 for the impurity magnetisation m(0 + ) in the spin-half two-channel Kondo model. Indeed, the values of both δ (l) and m(0 + ) point to the frustrated nature of the MCK problem and the absence of complete screening of the impurity moment at the ICFP.…”

Section: Local Marginal Fermi Liquid and Orthogonality Catastrophementioning

confidence: 94%

“…The screening manifests as an initial increase at temperatures below the Kondo temperature, followed by a saturation of the resistivity of the metal [1,13], and in the saturation of the impurity contribution to the magnetic susceptibility at low temperatures [6][7][8]. Generalisations of this model are obtained by taking impurities of higher spin [2,9,14], adding interactions between them [15][16][17][18][19][20][21], by promoting the model to a lattice of Kondo impurities [22][23][24][25][26] or by considering the case of a correlated host metal [27]. One can also construct multi-channel Kondo (MCK) models by allowing K conduction electron channels (K > 1) to interact with a spin-S d impurity [14,28,29] via a common exchange coupling J .…”

Section: Introductionmentioning

confidence: 99%

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

Patra

Mukherjee

et al. 2023

J. Phys.: Condens. Matter

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We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalization group (URG) 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. 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 non-Fermi liquids 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.

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“…J H is a Heisenberg coupling for the localized spins which was introduced in Ref. [45] in order to investigate the possibility of a spin liquid phase.…”

Section: A Model Hamiltonianmentioning

confidence: 99%

Spiral magnetism and chiral superconductivity in Kondo-Hubbard triangular lattice model

Ndiaye,

Dione,

Traor/'e

et al. 2021

Preprint

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Building on the results of Ref. [1], which identified an antiferromagnetic and Kondo singlet phases on the Kondo-Hubbard square lattice, we use the variational cluster approximation (VCA) to investigate the competition between these phases on a two-dimensional triangular lattice with 120 o spin orientation. In addition to the antiferromagnetic exchange interaction J ⊥ between the localized (impurity) and conduction (itinerant) electrons, our model includes the local repulsion U of the conduction electrons and the Heisenberg interaction J H between the impurities. At half-filling, we obtain the quantum phase diagrams in both planes (J ⊥ , UJ ⊥ ) and (J ⊥ , J H ). We identify a long-range, three-sublattice, spiral magnetic order which dominates the phase diagrams for small J ⊥ and moderate U, while a Kondo singlet phase becomes more stable at large J ⊥ . The transition from the spiral magnetic order to the Kondo singlet phase is a second-order phase transition. In the (J ⊥ , J H ) plane, we observe that the effect of J H is to reduce the Kondo singlet phase, giving more room to the spiral magnetic order phase. It also introduces some small magnetic oscillations of the spiral magnetic order parameter. At finite doping and when spiral magnetism is ignored, we find superconductivity with symmetry order parameter d + id, which breaks time reversal symmetry. The superconducting order parameter has a dome centered at around 5% hole doping, and its amplitude decreases with increasing J ⊥ . We show that spiral magnetism can coexist with d + id state and that superconductivity is suppressed, indicating that these two phases are in competition.

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Frustrated Kondo impurity triangle: A simple model of deconfinement

Cited by 12 publications

References 84 publications

From Liverpool to Beijing and Chongqing: William Band’s Adventure in Wartime China

From Liverpool to Beijing and Chongqing: William Band’s Adventure in Wartime China

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

Spiral magnetism and chiral superconductivity in Kondo-Hubbard triangular lattice model

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