We study two (very) weakly-coupled Hubbard chains in the half-filled case, and especially the situation where the intrachain Mott scale $m$ is much larger than the bare single-electron interchain hopping $t_{\perp}$ . First, we find that the divergence of the intrachain Umklapp channel at the Mott transition results in the complete vanishing of the single-electron interchain hopping: This is significant of a strong confinement of coherence along the chains. Excitations are usual charge fermionic solitons and spinon pairs of the Heisenberg chain. Then, we show rigorously how the tunneling of spinon-pairs produces a magnetic interchain exchange $J_{\perp}={t_{\perp}}^2/m>0$ . The result is an insulating state with spin-gapped excitations as in the delocalized limit (i.e. for rather large interchain hoppings), where the two-leg ladder is in the well-known D-Mott phase. Unlike for Bechgaard salts, the confinement/deconfinement transition at absolute zero is here a simple crossover: no metallic phase is found in undoped two-leg ladders. This statement might be generalized for N-leg ladders with N=3,4... (but not too large).We study two (very) weakly-coupled Hubbard chains in the half-filled case, and especially the situation where the intrachain Mott scale $m$ is much larger than the bare single-electron interchain hopping $t_{\perp}$. First, we find that the divergence of the intrachain Umklapp channel at the Mott transition results in the complete vanishing of the single-electron interchain hopping: This is significant of a strong confinement of coherence along the chains. Excitations are usual charge fermionic solitons and spinon pairs of the Heisenberg chain. Then, we show rigorously how the tunneling of spinon-pairs produces a magnetic interchain exchange $J_{\perp}={t_{\perp}}^2/m>0$. The result is an insulating state with spin-gapped excitations as in the delocalized limit (i.e. for rather large interchain hoppings), where the two-leg ladder is in the well-known D-Mott phase. Unlike for Bechgaard salts, the confinement/deconfinement transition at absolute zero is here a simple crossover: no metallic phase is found in undoped two-leg ladders. This statement might be generalized for N-leg ladders with N=3,4... (but not too large).

Jun 14, 20000 citations

Numerical studies of the 2-leg hubbard ladder

Douglas J. Scalapino

Physica C SuperconductivityAug 1, 19976 citations

Quantum phase transitions in a quarter-filled Hubbard ladder

R. Citro, E. Orignac

Physica C SuperconductivityApr 9, 20041 citation

Weakly coupled Hubbard chains at half-filling and confinement

Karyn Le Hur

We study two (very) weakly coupled Hubbard chains in the half-filled case, and especially the situation where the intrachain Mott scale m is much larger than the (bare) single-electron interchain hopping ${t}_{\ensuremath{\perp}}.$ First, we find that the divergence of the intrachain umklapp channel at the Mott transition results in the complete vanishing of the single-electron interchain hopping: this is significant of a strong confinement of coherence along the chains. Excitations are usual charge fermionic solitons and spinon-(anti)spinon pairs of the Heisenberg chain. Then, we show rigorously how the tunneling of spinon-(anti)spinon pairs produces an antiferromagnetic interchain exchange of the order of ${J}_{\ensuremath{\perp}}{=t}_{\ensuremath{\perp}}^{2}/m.$ In the ``confined'' phase and in the far infrared, the system behaves as a pure spin ladder. The final result is an insulating ground state with spin-gapped excitations exactly as in the opposite ``delocalized'' limit (i.e., for rather large interchain hoppings) where the two-leg ladder is in the well-known insulating $D\ensuremath{-}\mathrm{Mott}$ phase. Unlike materials with an infinite number of coupled chains (Bechgaard salts), the confinement/deconfinement transition at absolute zero is here a simple crossover: no metallic phase is found in undoped two-leg ladders. This statement might be generalized for N-leg ladders with $N=3,4,\dots{}$ (but not too large).We study two (very) weakly coupled Hubbard chains in the half-filled case, and especially the situation where the intrachain Mott scale m is much larger than the (bare) single-electron interchain hopping ${t}_{\ensuremath{\perp}}.$ First, we find that the divergence of the intrachain umklapp channel at the Mott transition results in the complete vanishing of the single-electron interchain hopping: this is significant of a strong confinement of coherence along the chains. Excitations are usual charge fermionic solitons and spinon-(anti)spinon pairs of the Heisenberg chain. Then, we show rigorously how the tunneling of spinon-(anti)spinon pairs produces an antiferromagnetic interchain exchange of the order of ${J}_{\ensuremath{\perp}}{=t}_{\ensuremath{\perp}}^{2}/m.$ In the ``confined'' phase and in the far infrared, the system behaves as a pure spin ladder. The final result is an insulating ground state with spin-gapped excitations exactly as in the opposite ``delocalized'' limit (i.e., for rather large interchain hoppings) where the two-leg ladder is in the well-known insulating $D\ensuremath{-}\mathrm{Mott}$ phase. Unlike materials with an infinite number of coupled chains (Bechgaard salts), the confinement/deconfinement transition at absolute zero is here a simple crossover: no metallic phase is found in undoped two-leg ladders. This statement might be generalized for N-leg ladders with $N=3,4,\dots{}$ (but not too large).

arXiv:cond-mat/0006224Physical review. B, Condensed matterApr 4, 200124 citations

Doping evolution of charge and spin excitations in two-leg Hubbard ladders: Comparing DMRG and FLEX results

Alberto Nocera, Yan Wang, N. D. Patel +4 more

We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard $U$ values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.We study the magnetic and charge dynamical response of a Hubbard model in a two-leg ladder geometry using the density matrix renormalization group (DMRG) method and the random phase approximation within the fluctuation-exchange approximation (FLEX). Our calculations reveal that FLEX can capture the main features of the magnetic response from weak up to intermediate Hubbard repulsion for doped ladders, when compared with the numerically exact DMRG results. However, while at weak Hubbard repulsion both the spin and charge spectra can be understood in terms of weakly interacting electron-hole excitations across the Fermi surface, at intermediate coupling DMRG shows gapped spin excitations at large momentum transfer that remain gapless within the FLEX approximation. For the charge response, FLEX can only reproduce the main features of the DMRG spectra at weak coupling and high doping levels, while it shows an incoherent character away from this limit. Overall, our analysis shows that FLEX works surprisingly well for spin excitations at weak and intermediate Hubbard $U$ values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.

arXiv:1803.08597Physical review. B./Physical review. BMay 31, 201821 citations

We study two (very) weakly-coupled Hubbard chains in the half-filled case, and especially the situation where the intrachain Mott scale

m

is much larger than the bare single-electron interchain hopping

t_{\perp}

. First, we find that the divergence of the intrachain Umklapp channel at the Mott transition results in the complete vanishing of the single-electron interchain hopping: This is significant of a strong confinement of coherence along the chains. Excitations are usual charge fermionic solitons and spinon pairs of the Heisenberg chain. Then, we show rigorously how the tunneling of spinon-pairs produces a magnetic interchain exchange

J_{\perp}={t_{\perp}}^2/m>0

. The result is an insulating state with spin-gapped excitations as in the delocalized limit (i.e. for rather large interchain hoppings), where the two-leg ladder is in the well-known D-Mott phase. Unlike for Bechgaard salts, the confinement/deconfinement transition at absolute zero is here a simple crossover: no metallic phase is found in undoped two-leg ladders. This statement might be generalized for N-leg ladders with N=3,4... (but not too large).

N=3,4,\dots{}

(but not too large).

U

values even in the difficult low-dimensional geometry such as a two-leg ladder. Finally, we discuss the implications of our results for neutron scattering and resonant inelastic x-ray scattering experiments on two-leg ladder cuprate compounds.