Frustrated Kondo impurity triangle: A simple model of deconfinement

Abstract

Deconfinement in gauge theories and symmetry-protected topological order are central to our understanding of strongly correlated quantum materials. A question of crucial importance regards the robustness of these concepts to the inclusion of fermionic matter fields. In light of this question, we study here a simple toy model, three antiferromagnetically coupled Kondo impurities, and demonstrate the existence of two distinct quantum phases which both preserve all symmetries of the model and thereby transcend the Landau-Ginzburg paradigm. An interpretation of the phase with dominant magnetic frustration in terms of symmetry protected topological order is corroborated by an irrational ground state degeneracy (suggestive of decoupled anyons) and a Wilson loop-like order parameter. We furthermore characterize the quantum transition between the two phases, which is driven by the proliferation of instantons in the emergent gauge field. Our work paves the way towards a better understanding of deconfinement in gauge theories interacting with matter fields.

Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models

“…In the last decades the role of magnetic frustration for HF has been discussed in the context of strongly correlated multi-impurity models [4,[33][34][35][36][37][38]. Since it was realized that the two-impurity problem lacks the complexity and the reported QCP appears to be an artifact of the approximation [11,12] made in the originally approach, nowadays the focus lies on models with three local moments coupled to an arbitrary number of conduction bands [33][34][35][36][37][38]. These papers in particular focus on the emergence of a frustration induced NFL fixed point that might be related to QCPs found in bulk materials.…”

“…In case of three identical correlated orbitals, the structure of the effective low-energy model reduces to four free parameters: The diagonal elements of ∆(−i0 + ) are equal for all impurities, whereas the off-diagonal elements ∆ off ij (−i0 + ) depend on the geometric arrangement of the impurities and the structure, as well as the filling, of the underlying lattice of the crystal. For Γ off ij = Im∆ off ij (−i0 + ) = 0 each of the correlated orbitals couples to its own, independent conduction band, as studied in [35]. In general, however, the impurities are coupled to the same conduction band, which implies Γ off ij = 0, such that a precursive diagonalization of Γ is necessary in order to obtain an "independent-bath" description of the model.…”

“…However, interesting physics can arises in problems that contain magnetically frustrated systems requiring at least three impurities [33-35, 37, 38]. Our mapping provides an ideal tool to investigate which physical condition the original model must fulfill in order to reach the critical parameter regimes reported for the trimer Kondo models [33][34][35][36][37][38].…”

“…Any approximative solution of multi-impurity problems, as toy model with regard to quantum criticality in HF therefore, need to ensure the absence of a QCP in the two impurity limit. Other examples of MIAM of the first kind are trimer models [33][34][35] involving three effective conduction bands.…”

“…The quest for a many-impurity problem that is solvable, and reveals interesting competing phases connected by a true QCP, triggered the investigation of the frustrated three impurity spin problems [33][34][35][36][37][38]. The connection to bulk materials, however, remains unclear, although it might be very helpful to illustrate the possibility of emerging complex phases.…”