Multiple Magnetization Plateaus and the Magnetic Structures in $S=1/2$ Heisenberg Model on the Checkerboard Lattice

TL;DR

This study investigates the ground state and magnetization plateaus of the $S=1/2$ Heisenberg model on a checkerboard lattice under magnetic field, revealing unique quantum structures and confirming some exact results.

Contribution

It provides detailed numerical analysis of magnetization plateaus and their magnetic structures, highlighting novel four-spin loop configurations not found in similar kagome lattice systems.

Findings

Identified magnetization plateaus at 0, 1/4, 3/8, 1/2, 3/4 of saturation.

Confirmed the 3/4 plateau state matches exact solutions.

Discovered unique four-spin quantum states in the 3/8 plateau with 16-fold degeneracy.

Abstract

We study the ground state of $S = 1/2$ Heisenberg model on the checkerboard lattice in a magnetic field by the density matrix renormalization group (DMRG) method with the sine-square deformation. We obtain magnetization plateaus at $M/M_{\rm sat}=$0, 1/4, 3/8, 1/2, and 3/4 where $M_{\rm sat}$ is the saturated magnetization. The obtained 3/4 plateau state is consistent with the exact result, and the 1/2 plateau is found to have a four-spin resonating loop structure similar to the six-spin loop structure of the 1/3 plateau of the kagome lattice. Different four-spin loop structures are obtained in the 1/4 and 3/8 plateaus but no corresponding states exist in the kagome lattice. The 3/8 plateau has a unique magnetic structure of three types of four-spin local quantum states in a $4\sqrt{2}\times2\sqrt{2}$ magnetic unit cell with a 16-fold degeneracy.