One-particle interchain hopping in a system of coupled Luttinger liquids is investigated using exact diagonalizations techniques. First, the two-chain problem of spinless fermions is studied in order to see the behavior of the band splitting as a function of the exponent $\ensuremath{\alpha}$ which characterizes the one-dimensional (1D) Luttinger liquid. Moderate intrachain interactions can lead to a strong reduction of this splitting. The onset of the confinement within the individual chains (defined by a vanishing splitting) seems to be governed by $\ensuremath{\alpha}$. We give numerical evidence that interchain coherent hopping can be totally suppressed for $\ensuremath{\alpha}\ensuremath{\sim}0.4$ or even smaller $\ensuremath{\alpha}$ values. The transverse conductivity is shown to exhibit a strong incoherent part. Even when coherent interchain hopping is believed to occur (at small $\ensuremath{\alpha}$ values), it is shown that the coherent Drude weight is always significantly smaller than the incoherent weight. Implications for the optical experiments in quasi-1D organic or high-
Tc superconductors are outlined.
Using grand canonical quantum Monte Carlo (QMC) simulations combined with maximum entropy analytic continuation, as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at half-filling. The one-particle spectral weight function, A(k,\ensuremath{\omega}), undergoes a qualitative change with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ associated with a transition from a four-band insulator to a two-band insulator. A simple analytical model based on the propagation of exact rung singlet states gives a good description of the features at large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. For smaller ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$, A(k,\ensuremath{\omega}) is similar to that of the one-dimensional model, with a coherent band of width the effective antiferromagnetic exchange J which is reasonably well described by renormalized spin-wave theory. The coherent band rides on a broad background of width several times the parallel hopping integral t, an incoherent structure similar to that found in calculations on both the one- and two-dimensional models. We also present QMC results for the two-particle spin and charge excitation spectra, and relate their behavior to the rung singlet picture for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and to the results of spin-wave theory for small ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$. \textcopyright{} 1996 The American Physical Society.
The T=0 phase diagram for two Hubbard chains with interchain hopping ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ and on-site repulsion U is derived within a renormalization-group (RG) approach. We explicitly allow for renormalization of the Fermi momenta. A nonzero ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ drives the chains towards strong coupling, and only for large ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ is a Luttinger liquid recovered. By use of weak-coupling RG, a qualitative picture of the phase diagram can be obtained. Our calculations show two different strong-coupling regimes: one with nonvanishing effective interchain hopping (〈${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$〉\ensuremath{\ne}0), not confining, for small U, and another with 〈${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$〉=0, confining, for large U. Numerical diagonalizations for a small cluster support the RG results.
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 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 and
g4 interactions, coherent interchain hopping coexists with anomalous scaling and non-Fermi liquid behavior in the chain direction.
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.
Using quantum Monte Carlo (QMC) simulations combined with Maximum Entropy analytic continuation as well as analytical methods, we examine the one- and two-particle dynamical properties of the Hubbard model on two coupled chains at small doping. The behavior of the single-particle spectral weight
A(k,ω) as a function of hopping anisotropy
t⊥/t at intermediate interaction strength is dominated by the transition from one-band behavior at large
t⊥/t to two-band behavior at small
t⊥/t, although interaction effects such as band-narrowing, a shift of spectral weight to higher energies in the unoccupied antibonding band and reflected structures due to short-range antiferromagnetic correlations are also present. A single-particle gap is resolved in the intermediate
t⊥/t Luther-Emery phase using Density Matrix Renormalization Group calculations. The dynamical spin and charge susceptibilities show features of the expected bonding-band Luttinger liquid behavior, as well as higher-energy features due to local excitations between the chains at large
t⊥/t, and evolve towards the behavior of two uncoupled chains as
t⊥/t is reduced. For the one hole, large
t⊥/t case, we make a detailed comparison between the QMC data and an approximation based on local rung states. At isotropic coupling and somewhat larger doping, we find that the dispersion of the single-particle bands is essentially unrenormalized from that of the noninteracting system, and that the spin and charge response functions have features also seen in random-phase-approximation calculations.