We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferroquadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. On the evidence of our numerical results, the quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be either a direct second order or a very weak first order transition.
We use a combination of analytical and numerical techniques to study the phase diagram of the frustrated Heisenberg model on the bilayer honeycomb lattice. Using the Schwinger-boson description of the spin operators followed by a mean-field decoupling, the magnetic phase diagram is studied as a function of the frustration coupling
J2 and the interlayer coupling ${J}_{\ensuremath{\perp}}$. The presence of both magnetically ordered and disordered phases is investigated by means of the evaluation of ground-state energy, spin gap, local magnetization, and spin-spin correlations. We observe a phase with a spin gap and short-range N\'eel correlations that survives for nonzero next-nearest-neighbor interaction and interlayer coupling. Furthermore, we detect signatures of a reentrant behavior in the melting of the N\'eel phase and symmetry restoring when the system undergoes a transition from an on-layer nematic valence-bond crystal phase to an interlayer valence-bond crystal phase. We complement our work with exact diagonalization on small clusters and dimer-series expansion calculations, together with a linear spin-wave approach to study the phase diagram as a function of the spin
S, the frustration, and the interlayer couplings.
We investigate the spatially anisotropic square lattice quantum antiferromagnet. The model describes isotropic spin-1/2 Heisenberg chains (exchange constant J) coupled antiferromagnetically in the transverse (J( perpendicular )) and diagonal (J(x)), with respect to the chain, directions. Classically, the model admits two ordered ground states-with antiferromagnetic and ferromagnetic interchain spin correlations-separated by a first-order phase transition at J( perpendicular )=2J(x). We show that in the quantum model this transition splits into two, revealing an intermediate quantum-disordered columnar dimer phase, both in two dimensions and in a simpler two-leg ladder version. We describe quantum-critical points separating this spontaneously dimerized phase from classical ones.
We overview some recent work and present new results on the ground-state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyse the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation in the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.
We overview some recent work and present new results on the ground-state properties and the spectrum of excitations of the two-dimensional frustrated Heisenberg antiferromagnet. Spontaneous dimer order is present in the quantum disordered phase of this model. We study the stability and analyse the structure of the spectrum, including the two-particle singlet excitation branch throughout the disordered phase, as well as in the vicinity of the Neel critical point. The variation in the dimer order parameter is also given, and it is argued that near the critical point it reflects the presence of the low-energy singlet bound state.
Bi
3Mn
4O
12(NO
3) is a recently synthesized spin-3/2 bilayer honeycomb antiferromagnet which behaves as a spin liquid down to very low temperatures. Beyond a magnetic field of about 5 T, it develops long-range N\'eel order. Motivated by this observation, we have studied spin-
S Heisenberg models with next neighbor frustrating interactions as well as bilayer couplings on the honeycomb lattice. For a model with frustrating second-neighbor exchange,
J2, we use a Lindemann-like criterion within spin-wave theory to show that N\'eel order melts beyond a critical
J2. The critical
J2 is found to increase in the presence of a magnetic field, implying the existence of a field-induced paramagnet-N\'eel transition over a range of parameters. For the bilayer model, we use a spin-
S generalization of bond operator mean-field theory to show that there is a N\'eel-dimer transition for various spin values with increasing bilayer coupling and that the resulting interlayer dimer state undergoes a field-induced transition into a state with transverse N\'eel order. Motivated by a broader interest in such paramagnets, we have also studied a spin-3/2 model which interpolates between the nearest-neighbor Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki (AKLT) parent Hamiltonian. Using exact diagonalization, we have found that there is a single N\'eel-AKLT quantum phase transition in this model. Computing the fidelity susceptibility and assuming a transition in the O(3) universality class, we have located the critical point of this model. In addition, we have obtained the spin gap of the AKLT parent Hamiltonian. Our numerics indicate that the AKLT state also undergoes a field-induced N\'eel ordering transition. We discuss implications of some of our results for experiments on Bi
3Mn
4O
12(NO
3) and for numerics on the honeycomb lattice Hubbard model.