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arXiv:cond-mat/9912372 · Physical review. B, Condensed matter

Low-energy dynamics of the one-dimensional multichannel Kondo-Heisenberg lattice

Natan Andrei, E. Orignac

Published Aug 1, 2000• 14 citations
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Abstract

We determine exactly the fixed point Hamiltonian of the one-dimensional multichannel Kondo-Heisenberg lattice model for any number of channels $N>~2.$ It is found to belong to a new class of non-Fermi-liquid fixed points, different from the usual Luttinger or Luther-Emery liquids. The fixed point describes an anomalous singlet with nontrivial internal dynamics manifesting itself in unconventional order. We compute the correlation functions of the various conventional and composite order parameters of the system, and find that for $N<~4$ the composite order parameters induce the dominant instabilities.

DOI
10.1103/physrevb.62.r3596

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We determine exactly the fixed point Hamiltonian of the one-dimensional multichannel Kondo-Heisenberg lattice model for any number of channels N> 2.N>~2.N> 2. It is found to belong to a new class of non-Fermi-liquid fixed points, different from the usual Luttinger or Luther-Emery liquids. The fixed point describes an anomalous singlet with nontrivial internal dynamics manifesting itself in unconventional order. We compute the correlation functions of the various conventional and composite order parameters of the system, and find that for N< 4N<~4N< 4 the composite order parameters induce the dominant instabilities.
We discuss a multichannel SU(N) Kondo model which displays nontrivial zero-temperature phase transitions due to a conduction electron density of states vanishing with a power law at the Fermi level. In a particular large- N limit, the system is described by coupled integral equations corresponding to a dynamic saddle point. We exactly determine the universal low-energy behavior of spectral densities at the scale-invariant fixed points, obtain anomalous exponents, and compute scaling functions describing the crossover near the quantum-critical points. We argue that our findings are relevant to recent experiments on impurity-doped d-wave superconductors.
A detailed and comprehensive study of the one-impurity multichannel Kondo model is presented. In the limit of a large number of conduction electron channels k>>1, the low-energy fixed point is accessible to a renormalization group improved perturbative expansion in 1/k. This straightforward approach enables us to examine the scaling, thermodynamics and dynamical response functions in great detail and make clear the following features: (i) the criticality of the fixed point, (ii) the universal non-integer degeneracy, and (iii) that the compensating spin cloud has a spatial extent of the order of one lattice spacing.
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 SSS. We present a detailed discussion for the two channel case and point out some possible non-Fermi-liquid behavior.
We study a one-dimensional electron gas in a special antiferromagnetic environment made by two spin-1/2 Heisenberg chains and a one-dimensional two-channel Kondo-Heisenberg lattice away from half-filling. These models flow to an intermediate fixed point which belongs to the universality class of chirally stabilized liquids. Using a Toulouse point approach, the universal properties of the models are determined as well as the identification of the leading instabilities. It is shown that these models exhibit a non-Fermi-liquid behavior with strong enhanced composite pairing correlations.
The $\ensuremath{\beta}$ function of the multichannel Kondo model is calculated exactly in the limit of large spin N and channel number $M=\ensuremath{\gamma}N$, with constant $\ensuremath{\gamma}$. There are no corrections in any finite order of 1/N1/N1/N. One zero is found at a finite coupling strength, showing directly the non-Fermi-liquid behavior of the model. This renormalization group flow allows introduction of a variational principle for the entropy, to obtain the low-temperature thermodynamics. Thus, in particular, the low-temperature thermodynamics of the noncrossing approximation to the Kondo model becomes accessible.
A multichannel Kondo system, where a single quantum spin couples to multiple channels of an electronic bath, provides one of the simplest examples of a zero-dimensional non-Fermi liquid. It is natural to ask: what happens when an extensive number of such systems are coupled together? A simple renormalization group argument implies that in a chain of SU(N) multichannel quantum systems, where each spin is coupled to its own bath of K channels, the individual spins dynamically decouple at low energy when N>K, resulting in a 'sliding' non-Fermi liquid. Using Quantum Monte Carlo (QMC) simulations, we find evidences of a continuous, 'dimensionality-changing' phase transition out of this non-Fermi liquid into a valence-bond solid phase as the intersite coupling is increased. Remarkably, at the critical point, correlations exhibit a power-law behavior even along the direction in which the spins are coupled, indicating the breakdown of dynamical decoupling at the transition. We also develop an RG scheme to understand the universal aspects of this transition.