Diagonal ladders: A class of models for strongly coupled electron systems

G. Sierra; M. A. Martín-Delgado; S. R. White; D. J. Scalapino; J. Dukelsky

doi:10.1103/PhysRevB.59.7973

Diagonal ladders: A class of models for strongly coupled electron systems

G. Sierra, M. A. Martín-Delgado, S. R. White, D. J. Scalapino, and J. Dukelsky

Phys. Rev. B 59, 7973 – Published 15 March 1999

Abstract

We introduce a class of models defined on ladders with a diagonal structure generated by $n_{p}$ plaquettes. The case $n_{p} = 1$ corresponds to the necklace ladder and has remarkable properties that are studied using density matrix renormalization-group and recurrent variational ansatzes. The antiferromagnetic Heisenberg (AFH) model on this ladder is equivalent to the alternating spin-1/spin- $\frac{1}{2}$ AFH chain, which is known to have a ferromagnetic ground state (GS). For doping 1/3 the GS is a fully doped (1,1) stripe with the holes located mostly along the principal diagonal while the minor diagonals are occupied by spin singlets. This state can be seen as a Mott insulator of localized Cooper pairs on the plaquettes. A physical picture of our results is provided by a $t_{p} - J_{p} - t_{d}$ model of plaquettes coupled diagonally with a hopping parameter $t_{d} .$ In the limit $t_{d} \to \infty$ we recover the original $t - J$ model on the necklace ladder while for a weak hopping parameter the model is easily solvable. The GS in the strong hopping regime is essentially an “on link” Gutzwiller projection of the weak hopping GS. We generalize the $t_{p} - J_{p} - t_{d}$ model to diagonal ladders with $n_{p} > 1$ and the two-dimensional square lattice. We use in our construction concepts familiar in statistical mechanics such as medial graphs and Bratelli diagrams.