Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice

Abstract

Using variational wave functions and Monte Carlo techniques, we study the antiferromagnetic Heisenberg model with first-neighbor $J_1$ and second-neighbor $J_2$ antiferromagnetic couplings on the honeycomb lattice. We perform a systematic comparison of magnetically ordered and nonmagnetic states (spin liquids and valence-bond solids) to obtain the ground-state phase diagram. Néel order is stabilized for small values of the frustrating second-neighbor coupling. Increasing the ratio $J_2/J_1$, we find strong evidence for a continuous transition to a nonmagnetic phase at $J_2/J_1\approx 0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence bond state gives an excellent approximation to the exact ground-state energy. For $0.23\lesssim J_2/J_1\lesssim 0.4$, a gapless $Z_2$ spin liquid with Dirac nodes competes with a plaquette valence-bond solid. In contrast, the gapped spin liquid considered in previous works has significantly higher variational energy. Although the plaquette valence-bond order is expected to be present as soon as the Néel order melts, this ordered state becomes clearly favored only for $J_2/J_1\gtrsim 0.3$. Finally, for $0.36\lesssim J_2/J_1\le 0.5$, a valence-bond solid with columnar order takes over as the ground state, being also lower in energy than the magnetic state with collinear order. We perform a detailed finite-size scaling and standard data collapse analysis, and we discuss the possibility of a deconfined quantum critical point separating the Néel antiferromagnet from the plaquette valence-bond solid.

arXiv comment10 pages, 12 figures

References in corpus (48)

• "Deconfined" quantum critical points
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Quantum Orders and Symmetric Spin Liquids
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Lieb-Schultz-Mattis in Higher Dimensions
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Wave function optimization in the variational Monte Carlo method
• An investigation of the quantum $J_1-J_2-J_3$ model on the honeycomb lattice
• Competing Spin Liquid States in the Spin-$1/2$ Heisenberg Model On Triangular Lattice
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Spiral order by disorder and lattice nematic order in a frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Gapless spin-liquid phase in an extended spin 1/2 triangular Heisenberg model
• Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice
• Nature of the spin liquid state of the Hubbard model on honeycomb lattice
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Magnetic order and paramagnetic phases in the quantum J1-J2-J3 honeycomb model
• Schwinger Boson Mean Field Theories of Spin Liquid States on Honeycomb Lattice: Projective Symmetry Group Analysis and Critical Field Theory
• 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
• Deconfined criticality in the frustrated Heisenberg honeycomb antiferromagnet
• Projective symmetry group classification of chiral spin liquids
• Bayesian Inference in the Scaling Analysis of Critical Phenomena
• Ground-state phase diagram of the quantum J1-J2 model on the honeycomb lattice
• Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Quantum critical phase with infinite projected entangled paired states
• Phase Diagram of the J1, J2, J3 Heisenberg Models on the Honeycomb Lattice: A Series Expansion Study
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• Site dilution of quantum spins in the honeycomb lattice
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Emergent honeycomb lattice in LiZn2Mo3O8
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Kernel method for corrections to scaling
• Valence-bond crystalline order in the $s=1/2$ $J_1$--$J_2$ model on the honeycomb lattice
• Some remarks on the Lieb-Schultz-Mattis theorem and its extension to higher dimensions
• Degeneracy of the ground-state of antiferromagnetic spin-1/2 Hamiltonians
• Spiral antiferromagnets beyond the spin-wave approximation: frustrated $XY$ and Heisenberg models in the honeycomb lattice
• Plaquette-RVB state in the Frustrated Honeycomb Antiferromagnet

Cited by in corpus (36)

• Thermal Hall effects in quantum magnets
• SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: implications for twistronics and Mott insulators
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Role of quantum fluctuations on spin liquids and ordered phases in the Heisenberg model on the honeycomb lattice
• Observation of plaquette fluctuations in the spin-1/2 honeycomb lattice
• Quantum Phases in the Honeycomb-Lattice $J_1$--$J_3$ Ferro-Antiferromagnetic Model
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Gapless spin liquids in disguise
• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Dynamical properties of Néel and valence-bond phases in the $J_1-J_2$ model on the honeycomb lattice
• Emergent Chiral Spin State in the Mott Phase of a Bosonic Kane-Mele-Hubbard Model
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Ground-state phase diagram of the frustrated spin-1/2 two-leg honeycomb ladder
• Symmetric spin liquids on the stuffed honeycomb lattice
• Spin dynamics and continuum spectra of the honeycomb J1-J2 antiferromagnetic Heisenberg model
• Deconfined Quantum Critical Point: A Review of Progress
• Classical phase diagram of the stuffed honeycomb lattice
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Nematic quantum phases in the bilayer honeycomb antiferromagnet
• Topological phase transition and nontrivial thermal Hall signatures in honeycomb lattice magnets
• Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu${}_7$TeO${}_4$(SO${}_4$)${}_5$Cl
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• A Multi-Purpose Platform for Analog Quantum Simulation
• Neural Network Approach to Scaling Analysis of Critical Phenomena
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• Topologically different spin disorder phases of the J1-J2 Heisenberg model on the honeycomb lattice
• An effective field theory approach for the $S=3/2$ bilayer honeycomb antiferromagnet
• Mean-field theory of interacting triplons in a two-dimensional valence-bond solid: stability and properties of many-triplon states
• Half-filled stripe to N$\acute{e}$el antiferromagnetism transition in the $t^{\prime }$-Hubbard model on honeycomb lattice
• Ground state and magnetic transitions of the orthorhombic antiferromagnet CaCo${}_2$TeO${}_6$
• Continuous transformation between ferro and antiferro circular structures in $J_1-J_2-J_3$ frustrated Heisenberg model
• 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
• Possible phases of the spin-$1/2$ $XXZ$ model on a honeycomb lattice by boson-vortex duality
• Partial Kondo Screening and Anomalous Thermal Conductance
• Demystifying quantum escapism on the honeycomb lattice
• Schwinger-Boson mean-field study of spin-1/2 $J_1$-$J_2$-$J_{\chi }$ model in honeycomb lattice: thermal Hall signature