Weakly coupled Hubbard chains at halffilling and confinement
Abstract
We study two (very) weakly coupled Hubbard chains in the halffilled case, and especially the situation where the intrachain Mott scale m is much larger than the (bare) singleelectron 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 singleelectron 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_{⊥}=t^{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 spingapped excitations exactly as in the opposite ``delocalized'' limit (i.e., for rather large interchain hoppings) where the twoleg ladder is in the wellknown insulating DMott 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 twoleg ladders. This statement might be generalized for Nleg ladders with N=3,4,... (but not too large).
 Publication:

Physical Review B
 Pub Date:
 April 2001
 DOI:
 10.1103/PhysRevB.63.165110
 arXiv:
 arXiv:condmat/0006224
 Bibcode:
 2001PhRvB..63p5110H
 Keywords:

 71.10.Pm;
 74.20.Mn;
 Fermions in reduced dimensions;
 Nonconventional mechanisms;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 12 pages, Part on (spinon) pairhopping amplitude extended in Appendix A