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arXiv:1005.0932 · Physical Review B

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, Gang Su

Published May 21, 2010• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.81.184427

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The spin-12\frac{1}{2}21​ 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 \ensuremathαc\ensuremath≃0.54{\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.54\ensuremathαc​\ensuremath≃0.54, where the quantum critical exponents \ensuremathν\ensuremath≃0.69(2)\ensuremath{\nu}\ensuremath{\simeq}0.69(2)\ensuremathν\ensuremath≃0.69(2) and \ensuremathγ\ensuremath≃1.363(8)\ensuremath{\gamma}\ensuremath{\simeq}1.363(8)\ensuremathγ\ensuremath≃1.363(8) are obtained. The quantum criticality is found to fall into the O(3)O(3)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.
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Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of onsite Hubbard repulsion. We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an SO(3)\mathrm{SO}(3)SO(3) order parameter (``chiral Heisenberg universality class''). Our calculation yields an estimate of the critical exponents $\ensuremath{\nu}\ensuremath{\simeq}1.31$, ${\ensuremath{\eta}}_{\ensuremath{\phi}}\ensuremath{\simeq}1.01$, and ${\ensuremath{\eta}}_{\ensuremath{\Psi}}\ensuremath{\simeq}0.08$, in reasonable agreement with the second-order expansion around the upper critical dimension. To test the validity of the present method, we use the conventional Gross-Neveu-Yukawa theory with Z2{\mathbb{Z}}_{2}Z2​ order parameter (``chiral Ising universality class'') as a benchmark system. We explicitly show that our functional RG approximation in the sharp-cutoff scheme becomes one-loop exact both near the upper as well as the lower critical dimension. Directly in 2+12+12+1 dimensions, our chiral Ising results agree with the best available predictions from other methods within the single-digit percent range for $\ensuremath{\nu}$ and ${\ensuremath{\eta}}_{\ensuremath{\phi}}$ and the double-digit percent range for ${\ensuremath{\eta}}_{\ensuremath{\Psi}}$. While one would expect a similar performance of our approximation in the chiral Heisenberg universality class, discrepancies with the results of other calculations here are more significant. Discussion and summary of various approaches is presented.
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