Motivated by the emergence of higher-order van Hove singularities (VHS) with power-law divergent density of states (DOS) $({\ensuremath{\rho}}_{c}(\ensuremath{\omega})={\ensuremath{\rho}}_{0}/{|\ensuremath{\omega}|}^{r}, 0<r<1)$ in materials, we investigate a multichannel Kondo model involving conduction electrons near the higher-order van Hove filling, termed power-law diverging multichannel Kondo model. This model considers
M channel and
N spin degrees of freedom. Employing a renormalization group analysis and dynamical large-
N approach, our results reveal the emergence of a pseudogap behavior in the spectral properties of the local impurity at the overscreened fixed point. We precisely determine the conditions under which the pseudogap behavior occurs, either by tuning the exponent
r or the ratio $\ensuremath{\kappa}=M/N$ to values such as
r∗ or ${\ensuremath{\kappa}}^{*}$. This pseudogap phase of spinon exhibits distinct physical properties that could have an impact on the properties of real systems. The results of this study provide novel insights into the pseudogap behaviors in strongly correlated systems and offer a playground to study the interplay between higher-order van Hove singularities and multichannel Kondo physics.
The traditional multichannel Kondo effect takes place when several gapless metallic electronic channels interact with a localized spin-
S impurity, with the number of channels
n exceeding the size of the impurity spin,
n>2S, leading to the emergence of non-Fermi liquid impurity behavior at low temperatures. Here, we show that the effect can be realized even when the electronic degrees of freedom are strongly correlated and gapped. The system under consideration consists of a single spin-
21 impurity coupled isotropically to
n spin singlet superconducting channels realized by one-dimensional leads with quasi-long-range superconducting order. The competition between the Kondo and superconducting fluctuations induces multiple distinct ground states and boundary phases depending on the relative strengths of the bulk and boundary interactions. Using the Bethe Ansatz technique, we identify four regimes: an overscreened Kondo phase, a zero-mode phase, a Yu-Shiba-Rusinov (YSR) phase, and a local-moment phase with an unscreened impurity, each with its own experimental characteristic. We describe the renormalization-group flow, the excitation spectrum, and the full impurity thermodynamics in each phase. Remarkably, even in the presence of a bulk mass gap, the boundary critical behavior in the Kondo phase is governed by the same exponents as in the gapless theory with the low-energy impurity sector flowing to the
SU(2)n Wess-Zumino-Witten (WZW) fixed point, and the impurity entropy monotonically decreasing as a function of temperature. In both the overscreened Kondo and zero-mode phases, the residual impurity entropy is
Simp(T→0)=ln[2cos(π/(n+2))]. In the YSR and unscreened phases on the other hand the impurity entropy exhibits non-monotonic temperature dependence and is effectively free at low temperatures with
Simp(T→0)=ln2.
We study the low-temperature thermodynamics of a spin-
S magnetic impurity coupled to
m> 2 degenerate bands of interacting electrons in one dimension. By exploiting boundary-conformal-field-theory techniques, we derive exact results for the possible impurity thermal and magnetic response. The leading behavior of the impurity magnetic susceptibility is shown to be insensitive to the electron-electron interaction. In contrast, there are two types of scaling behavior of the impurity specific heat consistent with the symmetries of the problem: Either it remains the same as for the ordinary multichannel Kondo problem for noninteracting electrons or it acquires a new leading term governed by a critical exponent ${\ensuremath{\alpha}}_{m}{=(g}_{m}^{\ensuremath{-}1}\ensuremath{-}1)/m,$ where
gm< 1 is a generalized (
m channel) Luttinger-liquid charge parameter measuring the strength of the repulsive electron-electron interaction. We conjecture that the latter behavior is indeed realized when the impurity is exactly screened
(m=2S).We study how the non-Fermi-liquid nature of the overscreened multichannel Kondo impurity model affects the response to a BCS pairing term that, in the absence of the impurity, opens a gap $\mathrm{\ensuremath{\Delta}}$. We find that the low-energy spectrum in the limit $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ actually does not correspond to the spectrum strictly at $\mathrm{\ensuremath{\Delta}}=0$. In particular, in the two-channel Kondo model, the $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$ ground state is an orbitally degenerate spin singlet, while it is an orbital singlet with a residual spin degeneracy at $\mathrm{\ensuremath{\Delta}}=0$. In addition, there are fractionalized spin-1/2 subgap excitations whose energy in units of $\mathrm{\ensuremath{\Delta}}$ tends toward a finite and universal value when $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$, as if the universality of the anomalous power-law exponents that characterize the overscreened Kondo effect turned into universal energy ratios when the scale invariance is broken by $\mathrm{\ensuremath{\Delta}}\ensuremath{\ne}0$. This intriguing phenomenon can be explained by the renormalization flow toward the overscreened fixed point and the gap cutting off the orthogonality catastrophe singularities. We also find other non-Fermi-liquid features at finite $\mathrm{\ensuremath{\Delta}}$: the local density of states lacks coherence peaks, the states in the continuum above the gap are unconventional, and the boundary entropy is a nonmonotonic function of temperature. The persistent subgap excitations are characteristic of the non-Fermi-liquid fixed point of the model, and thus depend on the impurity spin and the number of screening channels.
A novel large-
N limit of the multichannel Kondo model is introduced, for representations of the impurity spin described by Schwinger bosons. Three cases are found, associated with underscreening, overscreening, and exact Kondo screening of the impurity. The saddle-point equations derived in this limit are reminiscent of the ``noncrossing approximation,'' but preserve the Fermi-liquid nature of the model in the exactly screened case. Several physical quantities are computed, both numerically and analytically in the low- $\ensuremath{\omega},T$ limit, and compared to other approaches.
In the strong coupling limit, an effective resonant level model is derived for the spin-1 underscreened Kondo impurity model. A local quantum critical behavior is induced by the formation of a bound state with partially screened magnetic moment, displaying a residual
Z2 symmetry, leading to a
δ-resonance at the Fermi level in the impurity spectral function. As a consequence, a logarithmic singularity appears in the real part of the impurity dynamic spin susceptibility as a function of
max(ω,T), with
ω as frequency,
T temperature. A small magnetic field breaks this
Z2 symmetry and suppresses the singularity. We also discuss the possible manifestation of such a quantum critical behavior in the spin-1/2 two Kondo impurity model and the single quantum dot system with even electron occupation.