In our previous study, a single-branch of ferromagnetic magnon with linear dispersion is shown to exist near the (uncompensated) zigzag edge for Heisenberg model on honeycomb lattice. Here we develop a field-theory description for the edge magnon and find its dynamics is captured by the one-dimensional relativistic Klein-Gordon equation. It is intriguing that the boundary field theory for the edge magnon is tied up with its bulk counterpart, described by the two-dimensional Klein-Gordon equation. Furthermore, we also reveal how the parity symmetry relates evanescent modes on opposite edges in a honeycomb nanoribbon. By employing alternative methods, including Schwinger bosons and density-matrix renormalization group, we also demonstrate that the relativistic edge magnon is robust even when the Neel order in the bulk is destroyed by quantum fluctuations. The edge magnon is a direct consequence of uncompensated edge and may be verified in realistic materials by experimental probes.
Magnetic excitation in a spin dimer system on a bilayer honeycomb lattice is investigated in the presence of a zigzag edge, where disordered and ordered phases can be controlled by a quantum phase transition. In analogy with the case of graphene with a zigzag edge, a flat edge magnon mode appears in the disordered phase. In an ordered phase, a finite magnetic moment generates a mean-field potential to the magnon. Since the potential is nonuniform on the edge and bulk sites, it affects the excitation, and the dispersion of the edge mode deviates from the flat shape. We investigate how the edge magnon mode evolves when the phase changes through the quantum phase transition and discuss the similarities to ordered spin systems on a monolayer honeycomb lattice.
We examine the magnetic correlations in quantum spin models that were derived recently as effective low-energy theories for electronic correlation effects on the edge states of graphene nanoribbons. For this purpose, we employ quantum Monte Carlo simulations to access the large-distance properties, accounting for quantum fluctuations beyond mean-field-theory approaches to edge magnetism. For certain chiral nanoribbons, antiferromagnetic interedge couplings were previously found to induce a gapped quantum disordered ground state of the effective spin model. We find that the extended nature of the intraedge couplings in the effective spin model for zigzag nanoribbons leads to a quantum phase transition at a large, finite value of the interedge coupling. This quantum critical point separates the quantum disordered region from a gapless phase of stable edge magnetism at weak intraedge coupling, which includes the ground states of spin-ladder models for wide zigzag nanoribbons. To study the quantum critical behavior, the effective spin model can be related to a model of two antiferromagnetically coupled Haldane-Shastry spin-half chains with long-ranged ferromagnetic intrachain couplings. The results for the critical exponents are compared also to several recent renormalization-group calculations for related long-ranged interacting quantum systems.
In this work, a long-range resonating valence bond state is proposed as a variational wave function for the ground state of the
S=1/2 antiferromagnetic Heisenberg model on the honeycomb lattice. Employing Variational Monte Carlo (VMC) method, we show that the ground state energy obtained from such RVB wave function, lies well below the energy of the Néel state and compares very well to the energies evaluated from spin-wave theory and series expansion method. We also obtain the spin-spin correlation function along zig-zag and armchair directions and find that the two correlations are different, which indicates the anisotropic nature of the system. We compare our results with the square lattice and we show that although the quantum fluctuations on honeycomb lattice are much stronger, but do not completely destroy the magnetic order.
Motivated by the recent numerical evidence [Z. Meng, T. Lang, S. Wessel, F. Assaad, and A. Muramatsu, Nature (London) 464, 847 (2010)] of a short-range resonating valence bond state in the honeycomb lattice Hubbard model, we consider Schwinger boson mean field theories of possible spin liquid states on honeycomb lattice. From general stability considerations the possible spin liquids will have gapped spinons coupled to
Z2 gauge field. We apply the projective symmetry group method to classify possible
Z2 spin liquid states within this formalism on honeycomb lattice. It is found that there are only two relevant
Z2 states, differed by the value of gauge flux, zero or $\ensuremath{\pi}$, in the elementary hexagon. The zero-flux state is a promising candidate for the observed spin liquid and continuous phase transition into commensurate N\'eel order. We also derive the critical field theory for this transition, which is the well-studied O(4) invariant theory [A. V. Chubukov, T. Senthil, and S. Sachdev, Phys. Rev. Lett. 72, 2089 (1994); A. V. Chubukov, S. Sachdev, and T. Senthil, Nucl. Phys. B 426, 601 (1994); S. V. Isakov, T. Senthil, and Y. B. Kim, Phys. Rev. B 72, 174417 (2005)], and has an irrelevant coupling between Higgs and boson fields with cubic power of spatial derivatives as required by lattice symmetry. This is in sharp contrast to the conventional theory [S. Sachdev and N. Read, Int. J. Mod. Phys. B 5, 219 (1991)], where such transition generically leads to incommensurate magnetic order. In this scenario the
Z2 spin liquid could be close to a tricritical point. Soft boson modes will exist at seven different wave vectors. This will show up as low-frequency dynamical spin susceptibility peaks not only at the $\ensuremath{\Gamma}$ point (the N\'eel order wave vector) but also at Brillouin-zone-edge center
M points and twelve other points. Some simple properties of the $\ensuremath{\pi}$-flux state are studied as well. Symmetry allowed further neighbor mean field ansatz are derived in appendices which can be used in future theoretical works along this direction.
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.