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Progress of Theoretical Physics Supplement

Impurity Pinning of Spin Density Wave

Tôru Sakai

Published Jan 1, 2005• 0 citations
Publisher

Abstract

The collective excitations from the spin density wave pinned by some impurities are investigated with the self-consistent harmonic approximation applied for the phase Hamiltonian. It is found that the pinning-depinning transition due to the quantum fluctuation in the ground state cannot occur in two-dimensional nor three-dimensional isotropic system. In contrast, it has already been revealed that the quantum depinning (melting) can occur in one dimension. It suggests that the critical dimension of the quantum localization-delocalization phase transition is one, within the present approximation. The present result is also available for the charge density wave pinned by some impurities.

DOI
10.1143/ptps.157.148

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The collective excitations from the spin density wave pinned by some impurities are investigated with the self-consistent harmonic approximation applied for the phase Hamiltonian. It is found that the pinning-depinning transition due to the quantum fluctuation in the ground state cannot occur in two-dimensional nor three-dimensional isotropic system. In contrast, it has already been revealed that the quantum depinning (melting) can occur in one dimension. It suggests that the critical dimension of the quantum localization-delocalization phase transition is one, within the present approximation. The present result is also available for the charge density wave pinned by some impurities.
The effect of impurities on a spin-density wave (SDW) state in one-dimensional interacting electron systems is investigated by applying a phase representation and the theory of the weak impurity pinning. With the help of numerical simulation, it is shown that the pinned SDW is characterized by both a rapidly varying phase variable of the spin-density fluctuation and a slowly varying phase variable of the charge-density fluctuation. Based on this, the critical condition on the magnitude of interactions for localization-delocalization transition is determined by use of the self-consistent harmonic approximation.
Electrons in one-dimensional disordered systems exhibit Anderson localization in the absence of mutual interactions. However the transition is possible between localized and delocalized state as the interaction is turned on. In this paper such interplay between Anderson localization and interactions has been examined for spin dependent Tomonaga model based on the phase Hamiltonian derived by the bosonization of the fermion field. The problem is the extention of the classical impurity pinning of the charge density wave to that of quantum systems with phase variables of not only charge but also spin. The critical value of the interaction constant has been derived by the use of selfconsistent-harmonic approximation to the nonlinearity.
Localization-delocalization transition has been examined for interacting one-dimensional fermion systems with the backward and the Umklapp scattering by use of the phase Hamiltonian. In this approach the localized state is represented as that where the phase variable of either charge or spin (or both of them) is pinned by impurities and then distorted spatially, i.e. glassy. The transition can be understood as the depinning process due to the quantum fluctuations and its boundary has been determined both from the localized region and from the delocalized region. The two different procedures are shown to yield same criterion for the transition.
Effects of random impurities on one-dimensional interacting electron systems are studied by use of the quantum Monte Carlo method and the phase variable representation of charge density and superconducting fluctuations. The impurities pin the phase variable of charge density fluctuation, whereas the quantum fluctuation around the pinned state reduces the pinning effect yielding increase of the superconducting fluctuation since the charge density and the superconducting fluctuations are complementary to each other. Such interplay between randomness and interactions is shown explicitly by calculating spatial dependence of quantum fluctuations, metastable states and correlation functions for superconductivity. Quantum character of metastable states is discussed. It is found that superconducting state is more sensitive to impurities than charge density wave state when the interaction between electrons is weak.
The low temperature phase diagram of 1D disordered quantum systems like charge or spin density waves, superfluids, and related systems is considered by a full finite T renormalization group approach for the first time. At zero temperature the consideration of quantum phase slips leads to a new scenario for the unpinning (delocalization) transition. In the strong pinning limit the model is solved exactly. At finite T a rich crossover diagram with various scaling regions is found which reflects the zero temperature quantum critical behavior.