Quantum phase transition, universality and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on honeycomb lattice

Abstract

The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling $J>0$ in armchair direction and ferromagnetic interaction $J^{\prime }<0$ in zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio $Q_2$ and spin stiffness $\rho$ in two directions for various coupling ratio $\alpha =J^{\prime }/J$ under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point ${\alpha }_c=-0.93$. Through the finite-size scaling analysis on $Q_2$, ${\rho }_x$ and ${\rho }_y$, we determined the critical exponent related to the correlation length $\nu$ to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing $\alpha$. A phase diagram in the coupling ratio $\alpha$-magnetic field $h$ plane is obtained, where four phases, including dimerized, stripe, canted stripe and polarized phases are identified. It is also unveiled that the temperature dependence of the specific heat $C(T)$ for different $\alpha$'s intersects precisely at one point, similar to that of liquid ${}^3$He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of $Q_2$, $\rho$ and $C(T)$ are carefully analyzed. The susceptibility is well compared with the experimental data to give the magnetic parameters of both compounds.

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Cited by in corpus (8)

• Gapless quantum spin liquid in a honeycomb $\Gamma$ magnet
• Few-body systems capture many-body physics: tensor network approach
• Quantum Monte Carlo Study on the Spin-1/2 Honeycomb Heisenberg Model with Mixing Antiferromagnetic and Ferromagnetic Interactions in External Magnetic Fields
• Entanglement and quantum correlations in the XX spin-$1/2$ honeycomb lattice
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Magnetic properties of a spin-1/2 octagonal lattice
• Quantum spin state stabilized by coupling with classical spins
• Quantum gapped state in a spin-1/2 distorted honeycomb-based lattice with frustration