Anyons in multichannel Kondo systems

Abstract

Fractionalized quasiparticles -anyons -bear a special role in present-day physics. At the same time, they display properties of interest both foundational, with quantum numbers that transcend the spin-statistics laws, and applied, providing a cornerstone for decoherence-free quantum computation. The development of platforms for realization and manipulation of these objects, however, remains a challenge. Typically these entail the zero-temperature ground-state of incompressible, gapped fluids. Here, we establish a strikingly different approach: the development and probing of anyon physics in a gapless fluid. The platform of choice is a chiral, multichannel, multi-impurity realization of the Kondo effect. We discuss how, in the proper limit, anyons appear at magnetic impurities, protected by an asymptotic decoupling from the fluid and by the emerging Kondo length scale. We discuss possible experimental realization schemes using integer quantum Hall edges. The gapless and charged degrees of freedom coexistent with the anyons suggest the possibility of extracting quantum information data by transport and simple correlation functions. To show that this is the case, we generalize the fusion ansatz of Cardy's boundary conformal field theory, now in the presence of multiple localized perturbations. The generalized fusion ansatz captures the idea that multiple impurities share quantum information non-locally, in a way formally identical to anyonic zero modes. We display several examples supporting and illustrating this generalization and the extraction of quantum information data out of two-point correlation functions. With the recent advances in mesoscopic realizations of multichannel Kondo devices, our results imply that exotic anyon physics may be closer to reach than presently imagined. arXiv:1911.06336v1 [cond-mat.str-el]

Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

“…Four families of quasi codes realized in topological phases of matter. Some examples are fractional quantum Hall liquids and quantum spin liquids with gapped topological (TOP) order [48], various VBS models with gapped SPT order [51,53,54], some quantum dimer model [87] and defect model [88] with gapless TOP order, and both bosonic and fermionic models with gapless SPT order [89,90].…”

Floquet engineering multi-channel Kondo physics

“…While multi-channel Kondo impurities lead to the fascinating possibility of non-Abelian anyons [9][10][11], the multi-channel Kondo lattice is an open problem. The possible phases of a multi-channel Kondo lattice [8] range from magnetic and multipolar orders, where the conduction electrons decouple from the local moments, to non-Fermi liquids [13], symmetry-breaking heavy Fermi liquids (hastatic orders) [16][17][18], and finally, composite pair superconductivity [15,58].…”

“…This physics is already present in the single-channel Kondo model [7], and even richer physics is possible with multichannel interactions, where multiple, symmetry distinct flavors of conduction electrons screen the same local moment [8]. Multi-channel Kondo impurities are believed to realize non-Abelian anyons, including Majorana [9] and Fibonacci anyons [10,11] in the two-and three-channel cases, respectively. The multi-channel Kondo lattice likely includes non-Fermi liquid phases [12,13], superconductivity [14,15], channel symmetry breaking order [16][17][18] and even more exotic physics [19].…”

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

“…The leftover impurity degree of freedom, depicted as a blue filled circle in Fig. 1(a), takes the form of a Majorana fermion in the two-channel Kondo case 8,9 and of generalized nonabelian anyons for multiple channels 10,11 .…”