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arXiv:cond-mat/9401024 · Physical review. B, Condensed matter

Strong-coupling behavior of twot-Jchains with interchain single-electron hopping

Guang-Ming Zhang, Shiping Feng, Lu Yu

Published Apr 1, 1994• 3 citations
arXivHTMLPDF

Abstract

Using the fermion-spin transformation to implement spin-charge separation of constrained electrons, a model of two t-J chains with interchain single-electron hopping is studied by Abelian bosonization. After spin-charge decoupling the charge dynamics can be trivially solved, while the spin dynamics is determined by a strong-coupling fixed point where the correlation functions can be calculated explicitly. This is a generalization of the Luther-Emery line for two coupled t-J chains. The interchain single-electron hopping changes the asymptotic behavior of the interchain spin-spin correlation functions and the electron Green function, but their exponents are independent of the coupling strength.

DOI
10.1103/physrevb.49.9997

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A model of interacting electrons living on two chains coupled by a transverse hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ is solved exactly by a bosonization technique. It is shown that ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ does modify the shape of the Fermi surface also in the presence of interaction, although charge and spin excitations keep different velocities ${\mathit{u}}_{\mathrm{\ensuremath{\rho}}}$, ${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$. Two different regimes occur: At short distances, x\ensuremath{\ll}\ensuremath{\xi}=(${\mathit{u}}_{\mathrm{\ensuremath{\rho}}}$-${\mathit{u}}_{\mathrm{\ensuremath{\sigma}}}$)/4${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, the two chain model is not sensitive to ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, while for larger separation x\ensuremath{\gg}\ensuremath{\xi} interchain hopping is relevant and generates further singularities in the electron Green function besides those due to spin-charge decoupling.
The single-particle hopping between two chains is investigated by exact-diagonalization techniques supplemented by finite-size scaling analysis. In the case of two coupled strongly correlated chains of spinless fermions, the Taylor expansion of the expectation value of the single-particle interchain hopping operator of an electron at momentum kF{k}_{F}kF​ in powers of the interchain hopping ${t}_{\ensuremath{\perp}}$ is shown to become unstable in the thermodynamic limit. The single-chain anomalous exponent $\ensuremath{\alpha}$ [characterizing the low-energy density of state $N(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{\alpha}}]$ is shown to be the key parameter that governs the finite-size scaling behavior. In the regime $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{2p}$ $({\ensuremath{\alpha}}_{2p}\ensuremath{\simeq}0.41)$ where transverse two-particle hopping is less relevant than single-particle hopping, the finite-size effects can be described in terms of a universal scaling function. From this analysis it is found that the single-particle transverse hopping behaves as ${t}_{\ensuremath{\perp}}^{\ensuremath{\alpha}/(1\ensuremath{-}\ensuremath{\alpha})},$ in agreement with a random-phase-approximation--like treatment of the interchain coupling. For $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{2p},$ the scaling law is proved to change its functional form, thus signaling the onset of coherent transverse two-particle hopping.
The coherence of transport between two one-dimensional interacting Fermi liquids, coupled by single-particle hopping and interchain interaction, is examined in the context of two exactly soluble models. It is found that the coherence of the interchain hopping depends on the interplay between interchain hopping and interchain interaction terms, and not simply on the ground state spectral properties of an isolated chain. Specifically, the splitting of levels associated with interchain hopping in a g4{\mathrm{g}}_{4}g4​ soluble model is found to be enhanced by the introduction of interchain interaction. It is also shown that, for an exactly solvable model with both g2{\mathrm{g}}_{2}g2​ and g4{\mathrm{g}}_{4}g4​ interactions, coherent interchain hopping coexists with anomalous scaling and non-Fermi liquid behavior in the chain direction.
The one-particle Green's function for the two-chain Tomonaga–Luttinger (TL) model coupled by interchain hopping including spin degrees of freedom is calculated as a function of distance and time by the higher-dimensional bosonization method. In the short distance and time region, the one-dimensional TL liquid behavior is reproduced, while the long distance and time behavior is different from that for either TL or Fermi liquid. As the interaction becomes stronger, the behavior of Green's function becomes closer to that for the one-dimensional TL liquid, showing that the one-dimensionality is enhanced for stronger electron interaction, and is interpreted as the precursor of the “confinement”.
The coherence of transport between two one-dimensional interacting Fermi liquids, coupled by single-particle hopping and interchain interaction, is examined in the context of two exactly soluble models. It is found that the coherence of the interchain hopping depends on the interplay between interchain hopping and interchain interaction terms, and not simply on the ground state spectral properties of an isolated chain. Specifically, the splitting of levels associated with interchain hopping in a g(4) soluble model is found to be enhanced by the introduction of interchain interaction. It is also shown that, for an exactly solvable model with both g(2) and g(4) interactions, coherent interchain hopping coexists with anomalous scaling and non-Fermi liquid behavior in the chain direction.
Interchain hopping in systems of coupled chains of correlated electrons is investigated by exact diagonalization and quantum Monte Carlo methods. For two weakly coupled Hubbard chains at commensurate densities (e.g., n=1/3), the splitting at the Fermi level between bonding and antibonding bands is strongly reduced (but not suppressed) by repulsive interactions extending to a few lattice spacings. The magnitude of this reduction is directly connected to the exponent \ensuremath{\alpha} of the one-dimensional Luttinger liquid. However, we show that the incoherent part of the single-particle spectral function is much less affected by the interchain coupling. This suggests that incoherent interchain hopping could occur for intermediate \ensuremath{\alpha} values. \textcopyright{} 1996 The American Physical Society.