Dynamical properties of Néel and valence-bond phases in the $J_1-J_2$ model on the honeycomb lattice

Abstract

By using a variational Monte Carlo technique based upon Gutzwiller-projected fermionic states, we investigate the dynamical structure factor of the antiferromagnetic $S=1/2$ Heisenberg model on the honeycomb lattice, in presence of first-neighbor ($J_1$) and second-neighbor ($J_2$) couplings, for $J_2<0.5J_1$. The ground state of the system shows long-range antiferromagnetic order for $J_2/J_1\lesssim 0.23$, plaquette valence-bond order for $0.23\lesssim J_2/J_1\lesssim 0.36$, and columnar dimer order for $J_2/J_1\gtrsim 0.36$. Within the antiferromagnetic state, a well-defined magnon mode is observed, whose dispersion is in relatively good agreement with linear spin-wave approximation for $J_2=0$. When a nonzero second-neighbor super-exchange is included, a roton-like mode develops around the $K$ point (i.e., the corner of the Brillouin zone). This mode softens when $J_2/J_1$ is increased and becomes gapless at the transition point, $J_2/J_1\approx 0.23$. Here, a broad continuum of states is clearly visible in the dynamical spectrum, suggesting that nearly-deconfined spinon excitations could exist, at least at relatively high energies. For larger values of $J_2/J_1$, valence-bond order is detected and the spectrum of the system becomes clearly gapped, with a triplon mode at low energies. This is particularly evident for the spectrum of the dimer valence-bond phase, in which the triplon mode is rather well separated from the continuum of excitations that appears at higher energies.

References in corpus (5)

• "Deconfined" quantum critical points
• 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
• Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice

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• Spin dynamics and continuum spectra of the honeycomb J1-J2 antiferromagnetic Heisenberg model
• Magnetic properties of a spin-orbit entangled Jeff = 1/2 honeycomb lattice
• Disorder effects in spiral spin liquids: Long-range spin textures, Friedel-like oscillations, and spiral spin glasses
• Quantitative Determination of the Confinement and Deconfinement of spinons in the anomalous spectra of Antiferromagnets via the Entanglement Entropy
• Field-Induced Magnon Decay, Magnon Shadows, and Roton-like Excitations in the Honeycomb Antiferromagnet YbBr${}_3$
• Quantum decay of magnons in the unfrustrated honeycomb Heisenberg model
• The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach