Finite-size scaling and boundary effects in two-dimensional valence-bond-solids

Abstract

Various lattice geometries and boundaries are used to investigate valence-bond-solid (VBS) ordering in the ground state of an S=1/2 square-lattice quantum spin model---the J-Q model, in which 4- or 6-spin interactions Q are added to the Heisenberg exchange J. Ground state results for finite systems (with up to thousands of spins) are obtained using a projector QMC method. Great care has to be taken when extrapolating the order parameter to infinite size, in particular in cylinder geometry. Even though strong 2D VBS order exists and is established clearly with increasing system size on L*L lattices (or Lx* Ly lattices with a fixed Lx/Ly), only short-range VBS correlations are observed on long cylinders (when Lx -> infinity at fixed Ly). The correlation length increases with Ly, until long-range order sets in at a "critical" Ly. This width is large even when the 2D order is strong, e.g, for a system where the order parameter is 70% of the largest possible value, Ly=8 is required for ordering. Correlation functions for small L*L lattices can also be misleading. For a 20%-ordered system results for L up to 20 appear to extrapolate to a vanishing order parameter, while for larger L the behavior crosses over and extrapolates to a non-zero value (with exponentially small finite size corrections). The VBS order also exhibits interesting edge effects related to emergent U(1) symmetry, which, if not considered properly, can lead to wrong conclusions for the thermodynamic limit. The finite-size behavior for small L*L lattices and long cylinders is similar to that predicted for a Z2 spin liquid. The results raise concerns about recent works claiming Z2 spin liquid ground states in frustrated 2D systems, in particular, the Heisenberg model with nearest and next-nearest-neighbor couplings. VBS state in this system cannot be ruled out.

26 pages, 28 figures. v2: final, published version

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Cited by in corpus (65)

• Deconfined quantum critical points: symmetries and dualities
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Emergent $SO(5)$ Symmetry at the Néel to Valence-Bond-Solid Transition
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Deconfined criticality flow in the Heisenberg model with ring-exchange interactions
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Quantum Criticality and Spin Liquid Phase in the Shastry-Sutherland model
• Real-Space Parallel Density Matrix Renormalization Group
• $U(1)$-symmetric infinite projected entangled-pair state study of the spin-$1/2$ square $J_1-J_2$ Heisenberg model
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets
• Global symmetries, volume independence and continuity
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Random-Singlet Phase in Disordered Two-Dimensional Quantum Magnets
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Consistent scaling exponents at the deconfined quantum-critical point
• Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers
• Two-point resistance of a cobweb network with a $2r$ boundary
• Spin liquid versus dimer phases in an anisotropic J1-J2 frustrated square antiferromagnet
• RVB superconductors with fermionic projected entangled pair states
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Possible Nematic Spin Liquid in Spin-$1$ Antiferromagnetic System on the Square Lattice: Implication for the Nematic Paramagnetic State of FeSe
• Quantum Anomalous Hall Insulator Stabilized By Competing Interactions
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Quantum Monte Carlo study of mass-imbalanced Hubbard models
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Exotic continuous quantum phase transition between Z2 topological spin liquid and Neel order
• Magnetization plateaus of an easy-axis Kagomé antiferromagnet with extended interactions
• Entanglement entropy and deconfined criticality: emergent SO(5) symmetry and proper lattice bipartition
• Quantum criticality with emergent symmetry in the extended Shastry-Sutherland model
• Quantum phases of the frustrated XY models on the honeycomb lattice
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Chiral spin liquid and quantum phase diagram of spin-$1/2$ $J_1$-$J_2$-$J_{\chi }$ model on the square lattice
• Correlated valence-bond states
• Emergent topological excitations in a two-dimensional quantum spin system
• SU(N) Heisenberg model with multi-column representations
• Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
• Comparative study of the density matrix embedding theory for the Hubbard models
• Phase diagram and magnetic excitations of $J_1$-$J_3$ Heisenberg model on the square lattice
• Diagnosing order by disorder in quantum spin systems
• Sine-square deformation applied to classical Ising models
• Dual dynamic scaling in deconfined quantum criticality
• Comment on "Gapless spin liquid ground state of the spin-$\frac{1}{2}$ $J_1$-$J_2$ Heisenberg model on square lattices"
• One-dimensional projection of two-dimensional systems using spiral boundary conditions
• Class of variational ansaetze for the "spin-incoherent" ground-state of a Luttinger liquid coupled to a spin bath
• Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: stability and properties of many-triplon states
• Mechanics of nematic membranes: Euler-Lagrange equations, Noether charges, stress, torque and boundary conditions of the surface Frank nematic field
• Origin and stability of generalized Wigner crystallinity in triangular moiré systems
• Mott insulating states of the anisotropic SU(4) Dirac fermions
• Frustrated spin-$\frac{1}{2}$ Heisenberg magnet on an $AA$-stacked honeycomb bilayer: High-order study of the collinear magnetic phases of the $J_1$--$J_2$--$J_1^{\perp }$ model
• Study of the triangular-lattice Hubbard model with constrained-path quantum Monte Carlo
• Competition between Neel, Haldane nematic, plaquette valence bond solid, and $(\pi ,\pi )$ valence bond solid phases in SU(N) analogs of $S=1$ square-lattice antiferromagnets
• Specific heat and susceptibility of S=1/2 antiferromagnets on square, triangular, and kagome lattices
• Topological properties of a Valence-Bond-Solid
• Deconfined pseudocriticality in a model spin-1 quantum antiferromagnet