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

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 which are studied using DMRG and recurrent variational ansatzes. The AF Heisenberg model on this ladder is equivalent to the alternating spin-1/spin-1/2 AFH chain which is known to have a ferrimagnetic 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 $t_p-J_p$ 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 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 2D square lattice. We use in our construction concepts familiar in Statistical Mechanics as medial graphs and Bratelli diagrams.