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

2010/01/31 by Anders W. Sandvik · 10 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Logarithm #Materials science #Molecule #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum critical point #Quantum mechanics #Quantum phase transition #Scaling #Theoretical and Computational Physics #Valence (chemistry) #Valence bond theory #cond-mat.str-el #hep-lat

paper · pdf · doi:10.1103/physrevlett.104.177201

published as Phys. Rev. Lett. 104, 177201 (2010) · 4 pages, 5 figures, final published version

openalex publication_date 2010/04/26 · arxiv created 2010/04/29 · arxiv updated 2010/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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).

Citations

• Large-Nestimates of universal amplitudes of theCPN−1theory and comparison with aS=12square-lattice model with competing four-spin interactions
• Quantum phase transitions in the two-dimensionalJ1−J2model
• Theoretical estimates of the critical exponents of the superfluid transition inHe<mml:none/><mml:none/><mml:mprescripts/><mml:none/>4by lattice methods
• Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions
• Deconfined Quantum Critical Points

Cited by

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• Deconfined quantum criticality in spin-1/2 chains with long-range interactions
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Dual dynamic scaling in deconfined quantum criticality
• Deconfined criticality for the two-dimensional quantum S = 1-spin model with the three-spin and biquadratic interactions
• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• Deconfined Criticality Flow in the Heisenberg Model with Ring-Exchange Interactions
• First-Principles Simulations of 1+1D Quantum Field Theories at θ=π and Spin Chains
• Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: Stability and properties of many-triplon states
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets

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• Nature of the antiferromagnetic to valence-bond-solid quantum phase transition in a 2D XY-model with four-site interactions
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• SO(5) multicriticality in two-dimensional quantum magnets
• Quantum criticality with two length scales