N\'eel and Valence-Bond Crystal phases of the Two-Dimensional Heisenberg Model on the Checkerboard Lattice

TL;DR

This paper employs an improved tensor network method to analyze the ground states of the 2D Heisenberg model on the checkerboard lattice, revealing multiple magnetic and valence bond crystal phases as the coupling ratio varies.

Contribution

The study introduces an enhanced two-step DMRG approach projecting onto two-leg ladders, enabling detailed exploration of 2D isotropic models and their phase transitions.

Findings

Identification of four distinct ground-state phases with increasing J2.

Confirmation of a plaquette valence bond crystal at the isotropic point J2=J1.

Discovery of large energy gap (~0.67 J1) at the plaquette phase.

Abstract

I use an improved version of the two-step density matrix renormalization group method to study ground-state properties of the 2D Heisenberg model on the checkerboard lattice. In this version the Hamiltonian is projected on a tensor product of two-leg ladders instead of chains. This allows investigations of 2D isotropic models. I show that this method can describe both the magnetically disordered and ordered phases. The ground-state phases of the checkerboard model as $J_2$ increases are: (i) N\'eel with $Q=(\pi,\pi)$, (ii) a valence bond crystal (VBC) of plaquettes, (iii) N\'eel with $Q=(\pi/2,\pi)$, and (iv) a VBC of crossed dimers. In agreement with previous results, I find that at the isotropic point $J_2=J_1$, the ground state is made of weakly interacting plaquettes with a large gap $\Delta \approx 0.67 J_1$ to triplet excitations.