Weakly-coupled Hubbard chains at half-filling and Confinement

Abstract

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).

12 pages, Part on (spinon) pair-hopping amplitude extended in Appendix A; To appear in PRB

References in corpus (7)

• Bosonization and Strongly Correlated Systems
• Quantum Theory of the Smectic Metal State in Stripe Phases
• Two dimensional anisotropic non Fermi-liquid phase of coupled Luttinger liquids
• Optical conductivity of one-dimensional Mott insulators
• Phases of the two-band model of spinless fermions in one dimension
• Successive opening of the Fermi surface in doped N-leg Hubbard ladders
• Spinless fermions ladders at half filling

Cited by in corpus (19)

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• Generalized two-leg Hubbard ladder at half-filling: Phase diagram and quantum criticalities
• Coulomb drag between two spin incoherent Luttinger liquids
• The electron lifetime in Luttinger liquids
• Mott-Superfluid transition in bosonic ladders
• Spinon confinement: dynamics of weakly coupled Hubbard chains
• Competing orders in the generalized Hund chain model at half-filling
• Density-matrix renormalization group study of optical conductivity of the Mott insulator for two-dimensional clusters
• Interaction-induced Fermi surface deformations in quasi one-dimensional electronic systems
• Mott Transition in Quasi-One-Dimensional Systems
• Renormalization Group calculations with k|| dependent couplings in a ladder
• Possible phases of two coupled n-component fermionic chains
• Andreev scattering in the asymmetric ladder with preformed bosonic pairs
• From Luttinger to Fermi liquids in organic conductors
• Heavy electrons from Hund's rule and short-range Antiferromagnetism
• Conductivity between Luttinger liquids: coupled chains and bilayer graphene
• Mott transition in the Hubbard model on anisotropic honeycomb lattice with implications for strained graphene: Gutzwiller variational study