Quantum phase transition, O(3) universality class, and phase diagram of the spin- 12 Heisenberg antiferromagnet on a distorted honeycomb lattice: A tensor renormalization-group study

Wei Li, Shou-Shu Gong, Yang Zhao +1 more

arXiv:1005.0932Physical Review BMay 21, 201034 citations

Bulletin of the American Physical Society

Quantum Criticality in Coupled Spin-Dimer Systems

Stefan Weßel, S. C. Wenzel

Published Mar 17, 2010• 0 citations

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Quantum phase transition, O(3) universality class, and phase diagram of the spin- 12 Heisenberg antiferromagnet on a distorted honeycomb lattice: A tensor renormalization-group study

Wei Li, Shou-Shu Gong, Yang Zhao +1 more

The spin- $\frac{1}{2}$ Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the $O(3)$ universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.The spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the $O(3)$ universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.

arXiv:1005.0932Physical Review BMay 21, 201034 citations

Using the model of the DM interaction in

XY

antiferromagnetic spin chain with spin-phonon coupling, the nonadiabatic effects on the DM interaction have been studied by developing a nonadiabatic analytical approach. The results show that in the nonadiabatic case, to a certain finite phonon frequency, there exists a finite critical value of spin-phonon coupling. As the spin-phonon coupling decreases to the critical value, the system becomes gapless and the spin dimerization is destroyed. The DM interaction leads the system to have a finite critical value of spin-phonon coupling even in the adiabatic limit. The increase in staggered DM interaction will decrease the critical value of spin-phonon coupling, but increase that of phonon frequency, therefore, favors the dimerization. The nonadiabaticity plays an important role in suppressing the enhancement effects of the DM interaction to the dimerization. The dimerized ground state when DM interaction is present can be destroyed by the quantum lattice fluctuations. The threshold value of $\ensuremath{\beta}$ changing the effect of the DM interaction on the dimerization from suppression to promotion is not simply a constant but a crossover. For appropriate fixed values of spin-phonon coupling, phonon frequency and $\ensuremath{\beta}$, as

D

increases, the system undergoes a reentry of phase between spin-dimer state and gapless state.

The spin-

\frac{1}{2}

Heisenberg antiferromagnet on the distorted honeycomb (DHC) lattice is studied by means of the tensor renormalization-group method. It is unveiled that the system has a quantum phase transition of second order between the gapped quantum dimer phase and a collinear N\'eel phase at the critical point of coupling ratio ${\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54$, where the quantum critical exponents $\ensuremath{\nu}\ensuremath{\simeq}0.69(2)$ and $\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)$ are obtained. The quantum criticality is found to fall into the

O(3)

universality class. A ground-state phase diagram in the field-coupling ratio plane is proposed, where the phases such as the dimer, semiclassical N\'eel, and polarized phases are identified. A link between the present spin system to the boson Hubbard model on the DHC lattice is also discussed.