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Journal of Physics Condensed Matter

Spinless fermion chains with weak interchain hopping

J. Szṅajd, K. W. Becker

Published Nov 1, 2005• 5 citations
Publisher

Abstract

The linear renormalization-group transformation is used to study the thermodynamics of weakly coupled spinless fermion chains at half-filling. The model consists of a competing nearest-neighbour Coulomb repulsion and kinetic energy terms. The specific heat and the nearest-neighbour correlation function are studied as functions of temperature by varying the ratio of Coulomb repulsion to kinetic energy. The role of an interchain hopping is studied and the metal–insulator phase transition temperature as a function of hopping parameters is discussed.

DOI
10.1088/0953-8984/17/46/020

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The linear renormalization-group transformation is used to study the thermodynamics of weakly coupled spinless fermion chains at half-filling. The model consists of a competing nearest-neighbour Coulomb repulsion and kinetic energy terms. The specific heat and the nearest-neighbour correlation function are studied as functions of temperature by varying the ratio of Coulomb repulsion to kinetic energy. The role of an interchain hopping is studied and the metal–insulator phase transition temperature as a function of hopping parameters is discussed.
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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.
We use the density-matrix renormalization group to study the single-particle and two-particle correlation functions of spinless fermions in the ground state of a quarter filled ladder. This ladder consists of two chains having an in-chain extended Coulomb interaction reaching to third neighbor and coupled by interchain hopping. Within our short numerical coherence lengths, typically reaching 10 to 20 sites, we find a strong renormalization of the interchain hopping and the existence of a dimensional crossover at smaller interactions. We also find power exponents for single-particle hopping and interchain polarization consistent with the single chain. The total occupation correlation function has a larger power exponent and shows signs of a crossover from incoherent fermion hopping to coherent particle-hole pair motion between chains. We believe the ladder is gapless.
Intrachain and interchain local charge-transfer excitation spectra and the single-particle density of states are calculated in the spinless fermion model on a ladder with varying intrachain nearest-neighbor repulsion and interchain transfer integral at and near half filling by using the finite-temperature density-matrix renormalization-group method. Collective excitations are found to govern the low-energy intrachain spectra, while only individual local excitations are present in the interchain spectra. For strong intrachain repulsion, the low-energy motion of fermions is confined within a chain. The interchain motion of fermions is not bandlike but incoherent. As a consequence, the low-energy intrachain spectra are sensitive at half filling to the interchain transfer integral that weakens the density-density correlation along the chains. Similarly, the low-energy intrachain spectra are sensitive near half filling to the chemical potential that reduces the effect of the umklapp process. Similarities are pointed out between these findings and the experimentally observed, optical conductivity spectra in the quasi-one-dimensional organic conductors (TMTSF)2X.(\mathrm{TMTSF}{)}_{2}X.(TMTSF)2​X.