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⊥. 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⊥=t2⊥/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-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,... (but not too large).
Physical Review B
- Pub Date:
- April 2001
- Fermions in reduced dimensions;
- Nonconventional mechanisms;
- Condensed Matter - Strongly Correlated Electrons
- 12 pages, Part on (spinon) pair-hopping amplitude extended in Appendix A