Perturbative approach to the non-Fermi-liquid fixed point of the overscreened Kondo problem

Abstract

The non-Fermi-liquid fixed point of the overscreened Kondo problem is studied in the limit of a large number of conduction electron channels, k^> 1, using perturbation theory in \/k. By expanding the beta function and self-energy to sub-leading-order in \/k, we examine the scaling, thermodynamics, and dynamic response functions in detail. Our results compliment and extend previous work based on conformal field theory. We present the dynamical spin susceptibility for the first time and show that the impurity spin is marginally quenched, with an inelastic linewidth of order T.

Overscreened Kondo fixed point inS=1spin liquid

“…The coefficients C 1,2 are readily available in the literature 6,11,62 and are listed below in Eq. (20).…”

“…Likewise, it is possible to find an expression for fermionfermion, fermion-impurity and impurity-impurity susceptibilities 11 . Lastly, we list results for χ ′′ imp (ω, T )/ω which is a contribution to the NMR relaxation rate due to the impurity.…”

“…Since the original paper by Kondo 1 considering electron sea screening a single impurity spin, this problem has attracted significant theoretical and experimental attention. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] More recently, impurity physics has been studied in the context of strongly interacting systems. Numerous examples include 21 an impurity in systems with vanishing density of states 22,23 high temperature superconductors, 24 and quantum magnets.…”

“…when there are more channels than required to screen the impurity spin, the system has a non-Fermi-liquid fixed point. 6,7,9,11 This state is characterized by singularities in different physical observables, such as impurity spin susceptibility, specific heat, etc. It is particularly interesting as a solvable example of a system with a non-Fermi-liquid fixed point.…”

Solvable limit for the SU(N) Kondo model

“…This classic problem is now considered to be one of the class of condensed matter physics problems where a local degree of freedom interacts with a gap-less continuum. Some of the more powerful methods applied to understand properties of Kondo systems includes the renormalization group (RG) theory [2][3][4] , boundary conformal field theory (BCFT) 5 , an exact solution by Bethe Ansatz 6-8 , exact solutions using bosonization and canonical transformations [9][10][11] , and numerical methods 12 . With the advancement of new methods in micro-fabrication and other experimental techniques enabled physicists to design and fabricate artificial atoms in nano-structures.…”