Diagonal Ladders: A New Class of Models for Strongly Coupled Electron Systems

TL;DR

This paper introduces diagonal ladder models for strongly coupled electron systems, revealing novel ground states and phase behaviors through analytical and numerical methods, including DMRG, with implications for understanding Mott insulators and superconductivity.

Contribution

The paper presents a new class of diagonal ladder models, extending to 2D lattices, and analyzes their ground states and phase properties using advanced variational and statistical mechanics techniques.

Findings

Ground state is a ferrimagnetic AF Heisenberg model on the ladder.

Doped state forms a Mott insulator of localized Cooper pairs.

Strong hopping regime leads to a Gutzwiller-projected ground state.

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.