Mapping the Critical Point of the Two-Impurity Kondo Model to a Two-Channel Problem

Abstract

The two-impurity Kondo model with particle-hole symmetry is known to have a critical point at comparable RKKY interaction and Kondo temperature. Using bosonization and controlled low energy projection, we identify the critical point and map it to a solvable resonant level model. The physics of the critical point is shown to be the same as the two-channel Kondo model. An effective Hamiltonian is derived from which the solutions for the critical point and surrounding Fermi-liquid phase follow immediately.The universality of the critical point is strongly supported by the overall excellent agreement with the numerical renormalization group and conformal field theory results. PACS numbers: 75.20.Hr, 75.30.MbThe essence of the two-impurity Kondo model (TIKM) is the competition between Kondo effect and RKKY interaction [1 -4]. This competition is believed to be the core of many interesting properties of strongly correlated systems. Extensive numerical renormalization group (NRG) study on TIKM [5] revealed that the low energy behavior is of local Fermi-liquid (FL) type for most regions of the parameter space, except for a critical value of the RKKY interaction in the presence of particle-hole symmetry. The existence of the critical point was later put on firm ground by proving analytically the existence of a discontinuous point in the electron scattering phase shifts [6]. Although real systems are unlikely to fall right on the critical point, its presence, however, stipulates a new small energy scale,

Two-channel Kondo phases and frustration-induced transitions in triple quantum dots

“…62,65,66 The quantum critical point separating these phases is again the 2CK fixed point. 67,68 Triple quantum dot ͑TQD͒ models with three dots coupled to two leads in a mirror-symmetric fashion have also been studied, 14,15,18,34,64,69 recent work 34 by Žitko and Bonča showing in particular that a range of fixed points familiar from simpler quantum impurity models are accessible in a ring model. Indeed both two-channel and two-impurity Kondo effects are realized, on tuning the interdot couplings as a third dot is coupled to the two-impurity two-channel system.…”

Universal low-temperature crossover in two-channel Kondo models

“…In this paper we combine Abelian bosonization methods 17,27,28 with the powerful machinery of CFT 22,23 to obtain an exact description of the NFL to FL crossover in two-channel Kondo models. In particular, we calculate the full electron Green function at finite temperature, from which conductance follows.…”

Magnetic-field-induced quantum phase transitions in the two-impurity Anderson model

“…We note that there are some existing theoretical studies [18][19][20] targeting the double quantum dot, but they are limited to the cases with large magnetic fields, in which the physical properties follow the Zeeman splitting effect. [18][19][20] Although it is known that a local staggered magnetic field can induce a QPT as it directly couples to the critical staggered spin fluctuations, [12][13][14]16 the role of a local uniform magnetic field has not been explored. Such a uniform magnetic field is usually applied in experimental studies.…”

“…Interestingly, the two-impurity Anderson (or Kondo) model presents a minimal model for such a competition effect in an exactly solvable way. [9][10][11][12][13][14][15][16][17] With the Kondo coupling, the impurity spin forms a Kondo singlet state with the spins of the conduction electrons and a quasiparticle resonance peak develops at the Fermi energy, which is described by the Kondo effect. When the inter-impurity spin exchange interaction is antiferromagnetic and strong enough, the two impurity spins tend to form a singlet by themselves, against the formation of Kondo singlets, leading to the localization of quasiparticles.…”

“…The variation of C h also explains that χ predicted by either the conformal field theory 13 or the bosonization construction. 14,16 Compared with the two-channel QCP where T h ∼ h 228 , the analogy of the magnetic field in the two-channel Kondo impurity model is the staggered magnetic field in the two-impurity model, i.e., h s (S 1z − S 2z ), which directly couples to the critical staggered spin fluctuations. It is commonly anticipated that a staggered magnetic field h s is a relevant perturbation as it couples to S 1z − S 2z , the critical degrees of freedom.…”