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arXiv:1706.07810 · Physical review. B./Physical review. B

Competition between spin liquids and valence-bond order in the frustrated spin- 12 Heisenberg model on the honeycomb lattice

Francesco Ferrari, Samuel Bieri, Federico Becca

Published Sep 1, 2017• 46 citations
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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. N\'eel 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 ${J}_{2}/{J}_{1}\ensuremath{\approx}0.23$. Close to the transition point, the Gutzwiller-projected uniform resonating valence-bond state gives an excellent approximation to the exact ground-state energy. For $0.23\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\lesssim}0.36$, 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 N\'eel order melts, this ordered state becomes clearly favored only for ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.3$. Finally, for $0.36\ensuremath{\lesssim}{J}_{2}/{J}_{1}\ensuremath{\le}0.5$, 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 N\'eel antiferromagnet from the plaquette valence-bond solid.

DOI
10.1103/physrevb.96.104401

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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 < 0.5 J 1 . The ground state of the system shows long-range antiferromagnetic order for J 2 / J 1 ≲ 0.23 (Néel phase), plaquette valence-bond order for 0.23 ≲ J 2 / J 1 ≲ 0.36, and columnar dimer order for J 2 / J 1 ≳ 0.36. Within the Néel phase, 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 ≈ 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.
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