Spectral density for the elementary excitation of the multichannel Kondo model is investigated at finite temperatures with the use of the Bethe-ansatz method. Our formulation is based on the method of Yang and Yang developed in one-dimensional interacting boson systems. In the orbital singlet case, the narrow peak structure develops in the low-energy region as the temperature is decreased, whereas in the underscreened case, the excitation spectrum exhibits a divergence property at zero excitation energy, irrespective of the temperature. In the overscreened case, in which the non-Fermi-liquid fixed point is stable in the ground state, the peak structure develops in the low-energy region and the weight at zero excitation energy increases as the temperature is decreased. We discuss characteristic properties of the excitation spectrum in connection with bulk properties.
Elementary excitations for the integrable spin-S antiferromagnetic Heisenberg chain with an impurity spin are investigated by using the Bethe ansatz solution. Dressed holes are introduced in order to describe the elementary excitation. The characteristic energy dependence of the spectral density for the elementary excitation at zero temperature is discussed in connection with behaviour patterns of physical quantities. We extend our calculation for the elementary excitation to the case of finite temperatures, applying the method developed by Yang and Yang for one-dimensional interacting boson systems. At finite temperatures, in the case where , the spectral density shows a divergence property at zero excitation energy irrespective of the temperature, whereas in the case where , the peak structure develops in the low-energy region as the temperature is decreased.
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.
In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.
We solve the multichannel Kondo model with channel anisotropy using the Bethe ansatz method. The model generates energy scales, characterizing the neighborhoods of the various infrared fixed points, reflecting the structure of the symmetry breaking in the channel sector. The nature of these fixed points also depends on the magnitude of the impurity spin
S. We present a detailed discussion for the two channel case and point out some possible non-Fermi-liquid behavior.
We consider an atom in a double-well potential [parametrized by a two-level system (TLS)] interacting with screened conduction electrons. The tunneling of the TLS is assisted by the Fermi gas. Close to the strong-coupling fixed point the renormalization-group equations for the noncommutative model in the case of spinless fermions, but an arbitrary number of relevant orbital channels, lead to the n-channel Kondo problem with S=1/2. By solving the thermodynamic Bethe-ansatz equations for the n-channel Kondo problem numerically in the presence of a magnetic field, we discuss the low-temperature properties of the TLS close to the fixed point. The Zeeman splitting corresponds to the energy difference between the two positions of the tunneling atom. The atom is not localized at one of the potential minima. The susceptibility diverges as H\ensuremath{\rightarrow}0 and T\ensuremath{\rightarrow}0, indicating that the symmetric TLS is unstable against a local lattice deformation via coupling to phonons. The lattice distortion disappears above a critical temperature
Tc. The ground-state equilibrium situation of the TLS corresponds to H\ensuremath{\ne}0 and a Fermi-liquid picture applies. The values for the specific heat become very large as H\ensuremath{\rightarrow}0. For small fields the specific heat shows a double-peak structure, which is particularly pronounced for n=2.