arXiv:1001.4296 · Physical Review Letters

Continuous Quantum Phase Transition between an Antiferromagnet and a Valence-Bond Solid in Two Dimensions: Evidence for Logarithmic Corrections to Scaling

Anders W. Sandvik

Published Apr 26, 2010• 204 citations

Abstract

The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S=1/2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations. The results support a continuous transition of the ground state, in agreement with the theory of "deconfined" quantum criticality. There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated. This suggests that either the SU(N) symmetric noncompact CP;{N-1} field theory for deconfined quantum criticality has to be revised or that the theory for N=2 (as in the system studied here) differs significantly from N-->infinity (where the field theory is analytically tractable).

DOI: 10.1103/physrevlett.104.177201

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arXiv:1001.4296 · Physical Review Letters

Continuous Quantum Phase Transition between an Antiferromagnet and a Valence-Bond Solid in Two Dimensions: Evidence for Logarithmic Corrections to Scaling

Anders W. Sandvik

Published Apr 26, 2010• 204 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.104.177201

Related papers

Does quantum mechanics play a role in critical phenomena?

Rajiv R. P. Singh

The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S ¼ 1=2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations.The results support a continuous transition of the ground state, in agreement with the theory of ''deconfined'' quantum criticality.There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated.This suggests that either the SUðNÞ symmetric noncompact CP NÀ1 field theory for deconfined quantum criticality has to be revised or that the theory for N ¼ 2 (as in the system studied here) differs significantly from N ! 1 (where the field theory is analytically tractable).The antiferromagnetic to valence-bond-solid phase transition in the two-dimensional J-Q model (an S ¼ 1=2 Heisenberg model with four-spin interactions) is studied using large-scale quantum Monte Carlo simulations.The results support a continuous transition of the ground state, in agreement with the theory of ''deconfined'' quantum criticality.There are, however, large corrections to scaling, of logarithmic or very slowly decaying power-law form, which had not been anticipated.This suggests that either the SUðNÞ symmetric noncompact CP NÀ1 field theory for deconfined quantum criticality has to be revised or that the theory for N ¼ 2 (as in the system studied here) differs significantly from N ! 1 (where the field theory is analytically tractable).

PhysicsApr 26, 20109 citations

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From an antiferromagnet to a valence bond solid: evidence for a first-order phase transition

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Using a loop–cluster algorithm we investigate the spin- Heisenberg antiferromagnet on a square lattice with exchange coupling J and an additional four-spin interaction of strength Q . We confirm the existence of a phase transition separating antiferromagnetism at J / Q > J c / Q from a valence bond solid (VBS) state at J / Q < J c / Q . Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as 80 2 , we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J / Q > J c / Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at J / Q < J c / Q and we show that long but finite antiferromagnetic correlations are still present.Using a loop–cluster algorithm we investigate the spin- Heisenberg antiferromagnet on a square lattice with exchange coupling J and an additional four-spin interaction of strength Q . We confirm the existence of a phase transition separating antiferromagnetism at J / Q > J c / Q from a valence bond solid (VBS) state at J / Q < J c / Q . Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as 80 2 , we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J / Q > J c / Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at J / Q < J c / Q and we show that long but finite antiferromagnetic correlations are still present.

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To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU( $N$ ) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU( $N$ ) N\'eel and valence-bond solid phases is characterized for $N=2$ , 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ( $L=256$ ) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y\ensuremath{\equiv}1/\ensuremath{\nu}$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field ${\ensuremath{\Psi}}^{2}$ for the SU(3) model.To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU($N$) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU($N$) N\'eel and valence-bond solid phases is characterized for $N=2$, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size ($L=256$) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y\ensuremath{\equiv}1/\ensuremath{\nu}$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field ${\ensuremath{\Psi}}^{2}$ for the SU(3) model.

arXiv:1307.0501Physical Review BDec 13, 2013116 citations

We investigate the boundary phases of a (2+1)-dimensional quantum critical Heisenberg model with a dangling spin chain. By introducing a multispin

Q

-term along the boundary, we drive a continuous boundary transition from an antiferromagnetic (AF) order to a valence-bond solid (VBS) order. Using large-scale quantum Monte Carlo simulations, we locate the critical point at

Q_{c}=0.310(11)

, and obtain the critical exponents at

Q_{c}

, including

y_{s}=0.81(4)

and the scaling dimensions of AF and VBS order parameters

Δ_{s}=0.660(15)

and

Δ_{v}=0.204(14)

. The weak long-range AF order for $Q

N

is reduced to

2

in the field theoretical description of these deconfined critical points.

To examine the validity of the scenario of the deconfined critical phenomena, we carry out a quantum Monte Carlo simulation for the SU(

N

) generalization of the Heisenberg model with four-body and six-body interactions. The quantum phase transition between the SU(

N

) N\'eel and valence-bond solid phases is characterized for

N=2

, 3, and 4 on the square and honeycomb lattices. While finite-size scaling analysis works well up to the maximum lattice size (

L=256

) and indicates the continuous nature of the phase transition, a clear systematic change towards the first-order transition is observed in the estimates of the critical exponent $y\ensuremath{\equiv}1/\ensuremath{\nu}$ as the system size increases. We also confirm the relevance of a squared valence-bond solid field ${\ensuremath{\Psi}}^{2}$ for the SU(3) model.