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

TL;DR

This study investigates quantum phase transitions, universality, and scaling in a spin-1/2 Heisenberg model on a honeycomb lattice with competing ferromagnetic and antiferromagnetic interactions, revealing a transition in the O(3) universality class and complex phase behavior.

Contribution

It provides a detailed analysis of the quantum critical point, phase diagram, and scaling behaviors in a honeycomb lattice Heisenberg model with competing interactions, including comparison with experimental data.

Findings

Quantum phase transition at α_c = -0.93 from dimerized to stripe phase.

Critical exponent ν ≈ 0.7212 indicating O(3) universality.

Temperature-dependent specific heat curves intersect at a single point.

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 $J'<0$ 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 $\alpha=J'/J$ 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.