Quantum phase transition, universality, and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on a 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 ′ < 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 ρ in two directions for various coupling ratio α = 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 α c = −0.93. Through the finite-size scaling analysis on Q 2 , ρ x and ρ y , we determined the critical exponent related to the correlation length ν 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 α. A phase diagram in the coupling ratio α-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 α'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 , ρ and C(T ) are carefully analyzed. The susceptibility is well compared with the experimental data to give the magnetic parameters of both compounds.

Gapless quantum spin liquid in a honeycomb Γ magnet

“…9 and 11). Therefore, the DMRG result supports an intermediate region that impedes a direct transition between the zigzag and stripy phases 50,51 . For comparison, we also depict the spin-wave energy of the zigzag order (green belt) and stripy order (blue belt) in Fig.…”

The XYZ model in the mean-field approximation in terms of Pauli spin matrices

“…We are now ready to calculate the magnetization components. Let us start with the calculation of the zth component of magnetization M z by using (16) in which the denominator is already calculated to be the partition function given in Eq. ( 14), and now the numerator must be obtained, the details of which are given in the Appendix, and found as…”

“…The ground-state properties of the quasi-one-dimensional AFM Heisenberg model were investigated by using a variational method [15]. The quantum phase transition, scaling behaviours, and thermodynamics on a honeycomb lattice were systematically studied using the continuous-time quantum MC method [16]. Magnetization plateau and supersolid phases were analyzed in the AFM Heisenberg model on a tetragonally distorted fcc lattice [17].…”

Entanglement and quantum correlations in the XX spin-1/2 honeycomb lattice

“…The existence of plateau states are reported in the magnetization process in this model. Also, the spin-1/2 dimerized model on a honeycomb lattice with antiferromagnetic and ferromagnetic interactions is systematically studied using the continuous-time quantum Monte Carlo method [24][25][26] .…”