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.

10 pages, 12 figures

References in corpus (14)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• Spin liquid phase of the $S=\frac{1}{2}$ $J_1-J_2$ Heisenberg model on the triangular lattice
• Bridging lattice-scale physics and continuum field theory with quantum Monte Carlo simulations
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• 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
• Plaquette-RVB state in the Frustrated Honeycomb Antiferromagnet

Cited by in corpus (24)

• Thermal Hall effects in quantum magnets
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ 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
• Valence-Bond Order in a Honeycomb Antiferromagnet Coupled to Quantum Phonons
• Spin dynamics and continuum spectra of the honeycomb J1-J2 antiferromagnetic Heisenberg model
• Deconfined Quantum Critical Point: A Review of Progress
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu${}_7$TeO${}_4$(SO${}_4$)${}_5$Cl
• A Multi-Purpose Platform for Analog Quantum Simulation
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• Neural Network Approach to Scaling Analysis of Critical Phenomena
• Phonon Dynamics in the Chiral Kitaev Spin Liquid
• An effective field theory approach for the $S=3/2$ bilayer honeycomb antiferromagnet
• Topologically different spin disorder phases of the J1-J2 Heisenberg model on the honeycomb lattice
• Ground state and magnetic transitions of the orthorhombic antiferromagnet CaCo${}_2$TeO${}_6$
• Half-filled stripe to N$\acute{e}$el antiferromagnetism transition in the $t^{\prime }$-Hubbard model on honeycomb lattice
• 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