Abstract
We study the ground-state phase diagrams and properties of spin-1/2 Heisenberg models on the diamond-like-decorated square and triangular lattices. The diamond-like-decorated square (triangular) lattice is a lattice in which the bonds of a square (triangular) lattice are replaced with diamond units. The diamond unit has two types of antiferromagnetic exchange interactions, and the ratio λ of the strength of the diagonal bond to that of the other four edges determines the ground-state properties. In particular, the macroscopically degenerated tetramer-dimer states, which are equivalent to the dimer covering states of the original lattices, are stabilized for λc < λ < 2, where the value of λc depends on the lattices. To determine the phase diagrams and boundaries λc, we employ the modified spin wave (MSW) method and the quantum Monte Carlo (QMC) method to estimate the ground-state energies of the ferrimagnetic states for λ < λc, where we can consider the mixed spin-1 and spin-1/2 Lieb-lattice and triangular Lieb-lattice Heisenberg antiferromagnets instead, and obtain λc(square)=0.974 and λc(triangular)=0.988. We also calculate the long-range order (LRO) parameters using the MSW and QMC methods and find the scaling relations where the spin reductions of each sublattice are inversely proportional to the number of sublattice sites. We prove these scaling relations by applying an infinitesimal uniform magnetic field. Furthermore, by examining the calculation process in the MSW, we clarify the mathematical structure behind the scaling relations for the sublattice LROs.
Highlights
The exploration of the frustration and quantum effects in the spin system has been one of the most interesting issues in condensed matter physics
We calculate the long-range order (LRO) parameters using the modified spin wave (MSW) and quantum Monte Carlo (QMC) methods and find the scaling relations where the spin reductions of each sublattice are inversely proportional to the number of sublattice sites
Using the Marshall-Lieb-Mattis theorem and the MSW theory, we focus on the total spin of the ground state and examine the mathematical structure behind the scaling relations for the sublattice LRO parameters.[10]
Summary
The exploration of the frustration and quantum effects in the spin system has been one of the most interesting issues in condensed matter physics. We investigate the ground-state phase diagrams and properties of spin-1/2 Heisenberg models on the diamond-like-decorated square and triangular lattices. In Eq (1), note that the energy of the bond spin-pair is measured from that of the singlet dimer For both the diamond-like-decorated square and triangular lattices, we obtain three types of ground-state phases: the dimer-monomer (DM) states for λ > 2, the macroscopically degenerated tetramer-dimer (MDTD) states for λc < λ < 2, and the ferrimagnetic states for λ < λc, where the value of λc depends on the lattices.
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