Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions

2006/11/30 by Anders W. Sandvik · 15 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Antiferromagnetism #Condensed matter physics #Ground state #Heisenberg model #Molecule #Monte Carlo method #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum critical point #Quantum mechanics #Quantum phase transition #Scaling #Spin (aerodynamics) #Theoretical and Computational Physics #Valence (chemistry) #Valence bond theory #cond-mat.str-el #cond-mat.supr-con

paper · pdf · doi:10.1103/physrevlett.98.227202

published as Phys. Rev. Lett. 98, 227202 (2007) · 4 pages, 5 figures. v2: typo in Fig. 2 corrected. v3: minor changes, published version

openalex publication_date 2007/06/01 · arxiv created 2007/07/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.

Citations

• Quantum phase transitions in the two-dimensionalJ1−J2model
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Continuous Quantum Phase Transitions
• Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions
• Quantum critical phenomena
• Hard-Core Bosons on the Kagome Lattice: Valence-Bond Solids and Their Quantum Melting
• High-precision finite-size scaling analysis of the quantum-critical point ofS=1∕2Heisenberg antiferromagnetic bilayers
• Valence-bond crystal phase of a frustrated spin-1/2 square-lattice antiferromagnet
• Plaquette valence-bond crystal in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Deconfined Quantum Critical Points

Cited by

• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Variational Quantum Monte Carlo Simulations with Tensor-Network States
• Coplanar order induced by emergent frustration
• Directed-Loop Quantum Monte Carlo Method for Retarded Interactions
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: The Parent State of Quantum Phases
• The (2 + 1)-d U(1) quantum link model masquerading as deconfined criticality
• Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model
• Critical behavior of the QED3-Gross-Neveu model: Duality and deconfined criticality
• Note on Wess-Zumino-Witten models and quasiuniversality in 2+1 dimensions
• Dirac Fermions with Competing Orders: Non-Landau Transition with Emergent Symmetry
• Three-dimensional monopole-free CPN−1 models
• Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice
• Field-driven quantum phase transitions in S=12 spin chains
• Consistent Scaling Exponents at the Deconfined Quantum-Critical Point*
• Tunable deconfined quantum criticality and interplay of different valence-bond solid phases*