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Journal of the Physical Society of Japan

Two Coupled Chains of Tomonaga Model

Hideo Yoshioka, Yoshikazu Suzumura

Published Dec 15, 1994• 4 citations
Publisher

Abstract

Two chains of spinless Tomonaga model coupled by a transverse hopping are investigated in terms of phase Hamiltonian where separation of Fermi momentum in the presence of the hopping is taken into account explicitly. It is shown that there appears a gap in one of the two excitations by using a renormalization group method. As a result, correlation of charge density wave with interchain ordering and out of phase between the chains (superconductivity with intrachain ordering and in phase between the chains) becomes the most dominant one in the case of the repulsive (attractive) intrachain interaction.

DOI
10.1143/jpsj.63.4298

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Two chains of spinless Tomonaga model coupled by a transverse hopping are investigated in terms of phase Hamiltonian where separation of Fermi momentum in the presence of the hopping is taken into account explicitly. It is shown that there appears a gap in one of the two excitations by using a renormalization group method. As a result, correlation of charge density wave with interchain ordering and out of phase between the chains (superconductivity with intrachain ordering and in phase between the chains) becomes the most dominant one in the case of the repulsive (attractive) intrachain interaction.
Two chains of interacting spinless fermions in the presence of interchain hopping are investigated by use of phase Hamiltonian based on bosonization method. Excitation spectrum and phase diagram at absolute zero temperature are obtained by means of renormalization group method. Momentum distribution functions are also calculated. It is shown that the interchain hopping gives rise to drastic effects on properties of ground state compared to interchain interaction and is crucial to appearance of ordered states in higher dimensions.
By applying the renormalization group method to two-coupled chains in the Tomonaga model, the role of interchain hopping has been studied in the entire energy region. The energy for a crossover from the perturbational regime to the relevant regime becomes smaller than that of the interchain hopping due to one-dimensional fluctuations of the mutual interaction. From the calculation of response functions for charge density waves and superconducting states, the phase diagram of dominant and subdominant states has been obtained in the plane of mutual interactions with fixed energy.
By applying the renormalization group method to two-coupled chains in the Tomonaga model, the role of interchain hopping has been studied in the entire energy region. The energy for a crossover from the perturbational regime to the relevant regime becomes smaller than that of the interchain hopping due to one-dimensional fluctuations of the mutual interaction. From the calculation of response functions for charge density waves and superconducting states, the phase diagram of dominant and subdominant states has been obtained in the plane of mutual interactions with fixed energy. Organic conductors, 1) which exhibit low dimensional fluctuations, have been studied by using the model of quasi-one-dimensional systems, where the role of the interchain hopping plays an important role. As a basic model for such a system, two-coupled chains of interacting electrons
We study the effect of a transverse hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ in two chains of both spinless and spinning repulsively interacting fermions, by means of renormalization group and bosonization techniques. We show that, independent of the presence of spin, ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ strongly modifies the asymptotic long-wavelength behavior of the two chains, opening gaps in the excitation spectra. The origin of the instability of the gapless Luttinger-liquid behavior is identified in the flavor (==chain index) anisotropy induced by ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. In the case of spinning fermions, it leads to dominant pair fluctuations, in spite of the repulsive interaction. The role of spin is further analyzed in a model of two coupled chains showing, in the absence of ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, spin-charge separation without anomalous exponents. We solve this model exactly by the bosonization technique, and we find that the interesting analytical properties induced by spin-charge separation persist in the presence of transverse hopping, although ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ does modify the shape of the Fermi surface. The asymptotic expression of the single-particle Green function is also obtained.
The effect of interchain hopping and interaction on Anderson localization has been investigated for two coupled chains of spinless fermions with nearest neighbor interaction. Using the renormalization group method, we find that interchain hopping plays a significant role when the correlation gap induced by the interplay of interchain hopping and intrachain interaction becomes larger than the Anderson localization energy scale induced by impurities. The strong competition between localization and delocalization is examined for attractive interaction.
The effect of interchain hopping and interaction on Anderson localization has been investigated for two coupled chains of spinless fermions with nearest neighbor interaction. Using the renormalization group method, we find that interchain hopping plays a significant role when the correlation gap induced by the interplay of interchain hopping and intrachain interaction becomes larger than the Anderson localization energy scale induced by impurities. The strong competition between localization and delocalization is examined for attractive interaction.