A local moment approach to the gapped Anderson model

We develop a non-perturbative local moment approach (LMA) for the gapped Anderson impurity model (GAIM), in which a locally correlated orbital is coupled to a host with a gapped density of states. Two distinct phases arise, separated by a level-crossing quantum phase transition: a screened singlet phase, adiabatically connected to the non-interacting limit and as such a generalized Fermi liquid (GFL); and an incompletely screened, doubly degenerate local moment (LM) phase. On opening a gap (δ) in the host, the transition occurs at a critical gap δ<Subscript>c</Subscript>, the GFL [LM] phase occurring for δ>δ<Subscript>c</Subscript> [ δ>δ<Subscript>c</Subscript>] . In agreement with numerical renormalization group (NRG) calculations, the critical δ<Subscript>c</Subscript>=0 at the particle-hole symmetric point of the model, where the LM phase arises immediately on opening the gap. In the generic case by contrast δ<Subscript>c</Subscript> > 0, and the resultant LMA phase boundary is in good quantitative agreement with NRG results. Local single-particle dynamics are considered in some detail. The major difference between the two phases resides in bound states within the gap: the GFL phase is found to be characterised by one bound state only, while the LM phase contains two such states straddling the chemical potential. Particular emphasis is naturally given to the strongly correlated, Kondo regime of the model. Here, single-particle dynamics for both phases are found to exhibit universal scaling as a function of scaled frequency ω/ω<Subscript>m</Subscript> <Superscript>0</Superscript> for fixed gaps δ/ω<Subscript>m</Subscript> <Superscript>0</Superscript>, where ω<Subscript>m</Subscript> <Superscript>0</Superscript> is the characteristic Kondo scale for the gapless (metallic) AIM; at particle-hole symmetry in particular, the scaling spectra are obtained in closed form. For frequencies |ω|/ω<Subscript>m</Subscript> <Superscript>0</Superscript> ≫δ/ω<Subscript>m</Subscript> <Superscript>0</Superscript>, the scaling spectra are found generally to reduce to those of the gapless, metallic Anderson model; such that for small gaps δ/ω<Subscript>m</Subscript> <Superscript>0</Superscript>≪ 1 in particular, the Kondo resonance that is the spectral hallmark of the usual metallic Anderson model persists more or less in its entirety in the GAIM. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008