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arXiv:1608.08327 · Physical review. B./Physical review. B

Multiple magnetization plateaus and magnetic structures in the S = 1 2 Heisenberg model on the checkerboard lattice

Katsuhiro Morita, Naokazu Shibata

Published Oct 10, 2016• 15 citations
arXivHTMLPDF

Abstract

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

DOI
10.1103/physrevb.94.140404

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We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaus for m=0,1/4,1/2m=0, 1/4, 1/2m=0,1/4,1/2, and 3/43/43/4, where mmm is the magnetization normalized by its saturation value. These incompressible states correspond to somewhat similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for m=0m=0m=0. Our results are based on exact diagonalization as well as density-matrix renormalization-group large-scale simulations and interpreted in terms of simple parameter-free trial wave functions.
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