Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like Decorated Square Lattice

Abstract

We study the ground-state phase diagram of a Heisenberg model with spin $S=\frac{1}{2}$ on a diamond-like decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio $\lambda$ between the length of the diagonal bond and that of the other four edges determines the strength of frustration. It has been pointed out [J. Phys. Soc. Jpn {\bf85}, 033705 (2016)] that the so-called tetramer-dimer states, which are expected to be stabilized in an intermediate region of ${\lambda }_{\mathrm{c}}<\lambda <2$, are identical to the square-lattice dimer covering states, which ignited renewed interest in high-dimensional diamond-like decorated lattices. In order to determine the phase boundary ${\lambda }_{\mathrm{c}}$, we employ the modified spin wave method to estimate the energy of the ferrimagnetic state and obtain ${\lambda }_{\mathrm{c}}=0.974$. Our obtained magnetizations for spin-$\frac{1}{2}$ sites and for spin-1 sites are $m=0.398$ and $\tilde{m}=0.949$, and spin reductions are 20 \% and 5\%, respectively. This indicates that spin fluctuation is much smaller than that of the $S=\frac{1}{2}$ square-lattice antiferromagnet: thus, we can consider that our obtained ground-state energy is highly accurate. Further, our numerical diagonalization study suggests that other cluster states do not appear in the ground-state phase diagram.

22 pages, 11 figures

References in corpus (5)

• Many-Body Physics with Ultracold Gases
• Exact Realization of a Quantum-Dimer Model in Heisenberg Antiferromagnets on a Diamond-Like Decorated Lattice
• Phase transitions of geometrically frustrated mixed spin-1/2 and spin-1 Ising-Heisenberg model on diamond-like decorated planar lattices
• Infinitely Multiple Steps in Magnetization of Ferro- and Antiferromagnetic Ising Models with Frustration on a Diamond Hierarchical Lattice
• Exact Solutions on the Ground States of Ising Models in Magnetic Fields with Frustration on a Diamond Hierarchical Lattice

Cited by in corpus (5)

• Phases of the spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in a magnetic field
• Thermal first-order phase transitions, Ising critical points, and reentrance in the Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field
• Quantum dimer model containing Rokhsar-Kivelson point expressed by spin-1/2 Heisenberg antiferromagnets
• Emergence of a Dimer-Dimer Interaction in the Low-Energy Effective Quantum-Dimer Model of a Diamond-Like-Decorated Square-Lattice Heisenberg Antiferromagnets with Further Neighbor Couplings
• Notes on Ground-State Properties of Mixed Spin-1 and Spin-1=2 Lieb-Lattice Heisenberg Antiferromagnets