We study the ground-state phase diagram of the quantum ${J}_{1}\ensuremath{-}{J}_{2}$ model on the honeycomb lattice by means of an entangled-plaquette variational ansatz. Values of energy and relevant order parameters are computed in the range $0\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}1$. The system displays classical order for ${J}_{2}/{J}_{1}\ensuremath{\lesssim}0.2$ (N\'eel) and for ${J}_{2}/{J}_{1}\ensuremath{\gtrsim}0.4$ (collinear). In the intermediate region, the ground state is disordered. Our results show that the reduction of the half-filled Hubbard model to the model studied here does not yield accurate predictions.
Using the coupled-cluster method for high orders of approximation and Lanczos exact diagonalization we study the ground-state phase diagram of a quantum spin-
21 J1-
J2 model on the square lattice with plaquette structure. We consider antiferromagnetic (
J1>0) as well as ferromagnetic (
J1<0) nearest-neighbor interactions together with frustrating antiferromagnetic next-nearest-neighbor interaction
J2>0. The strength of interplaquette interaction $\ensuremath{\lambda}$ varies between $\ensuremath{\lambda}=1$ (which corresponds to the uniform
J1-
J2 model) and $\ensuremath{\lambda}=0$ (which corresponds to isolated frustrated 4-spin plaquettes). While on the classical level ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) both versions of models (i.e., with ferro- and antiferromagnetic
J1) exhibit the same ground-state behavior, the ground-state phase diagram differs basically for the quantum case
s=1/2. For the antiferromagnetic case (
J1>0) N\'eel antiferromagnetic long-range order at small
J2/J1 and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.47$ as well as collinear striped antiferromagnetic long-range order at large
J2/J1 and $\ensuremath{\lambda}\ensuremath{\gtrsim}0.30$ appear which correspond to their classical counterparts. Both semiclassical magnetic phases are separated by a nonmagnetic quantum paramagnetic phase. The parameter region, where this nonmagnetic phase exists, increases with decreasing $\ensuremath{\lambda}$. For the ferromagnetic case (
J1<0) we have the trivial ferromagnetic ground state at small
J2/∣J1∣. By increasing
J2 this classical phase gives way for a semiclassical plaquette phase, where the plaquette block spins of length
s=2 are antiferromagnetically long-range ordered. Further increasing of
J2 then yields collinear striped antiferromagnetic long-range order for $\ensuremath{\lambda}\ensuremath{\gtrsim}0.38$, but a nonmagnetic quantum paramagnetic phase $\ensuremath{\lambda}\ensuremath{\lesssim}0.38$.
We studied the ground-state phase diagram of spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model on the square lattice with first-neighbor
J1 and second-neighbor
J2 antiferromagnetic interactions using both infinite density matrix renormalization group (iDMRG) and DMRG approaches. We show that a plaquette valence bond phase is realized in an intermediate region $0.50\ensuremath{\le}{J}_{2}/{J}_{1}<0.54$ between a N\'eel magnetic ordered phase at
J2/J1<0.50 and a stripy magnetic ordered phase at ${J}_{2}/{J}_{1}\ensuremath{\ge}0.54$. The plaquette valence bond phase is characterized by finite dimer orders in both the horizontal and vertical directions. Contrary to the spin-1/2 ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model, we do not find numerical evidence for a quantum spin liquid phase in the ${J}_{1}\text{\ensuremath{-}}{J}_{2} XY$ model.
The ground state phase of spin-1/2 J_1-J_2 antiferromagnetic Heisenberg model on square lattice in the maximally frustrated regime (J_2 ~ 0.5J_1) has been debated for decades. Here we study this model by using a recently proposed novel numerical method - the cluster update algorithm for tensor product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with the state of art exact diagonalization study, and the energy differences between these two studies are of the order of 10^{-3}J_1 per site. At the largest bond dimension available D (D=9), we find a paramagnetic ground state without any valence bond solid order in the thermodynamic limit in the range of 0.5 < J_2/J_1 < 0.6, which implies the emergence of a spin-liquid phase. Furthermore, we investigate the topologically ordered nature of such a spin-liquid phase by measuring a nonzero topological entanglement entropy.
We perform highly accurate density matrix renormalization group (DMRG) simulations to investigate the ground-state properties of the spin-
1/2 antiferromagnetic square lattice Heisenberg
J1-
J2 model. Based on studies of numerous long cylinders with circumferences of up to 14 lattice spacings, we obtain strong evidence for a topological quantum spin liquid state in the region $0.41\ensuremath{\le}{J}_{2}/{J}_{1}\ensuremath{\le}0.62$, separating conventional N\'eel and striped antiferromagnetic states for smaller and larger
J2/J1, respectively. The quantum spin liquid is characterized numerically by the absence of magnetic or valence bond solid order, and nonzero singlet and triplet energy gaps. Furthermore, we positively identify its topological nature by measuring a nonzero topological entanglement entropy $\ensuremath{\gamma}=0.70\ifmmode\pm\else\textpm\fi{}0.02$, extremely close to $\ensuremath{\gamma}=\mathrm{ln}(2)\ensuremath{\approx}0.69$ (expected for a
Z2 quantum spin liquid) and a nontrivial finite size dimerization effect depending upon the parity of the circumference of the cylinder. We also point out that a valence bond solid, and indeed any discrete symmetry breaking state, would be expected to show a constant correction to the entanglement entropy of opposite sign to the topological entanglement entropy.
We use the density matrix renormalization group (DMRG) algorithm to study the phase diagram of the spin-
21 Heisenberg model on a honeycomb lattice with first (
J1) and second (
J2) neighbor antiferromagnetic interactions, where a
Z2 spin liquid region has been proposed. By implementing SU(2) symmetry in the DMRG code, we are able to obtain accurate results for long cylinders with a width slightly over 15 lattice spacings and a torus up to the size $N=2\ifmmode\times\else\texttimes\fi{}6\ifmmode\times\else\texttimes\fi{}6$. With increasing
J2, we find a N\'eel phase with a vanishing spin gap and a plaquette valence-bond (PVB) phase with a nonzero spin gap. By extrapolating the square of the staggered magnetic moment
ms2 on finite-size cylinders to the thermodynamic limit, we find the N\'eel order vanishing at ${J}_{2}/{J}_{1}\ensuremath{\simeq}0.22$. For $0.25<{J}_{2}/{J}_{1}\ensuremath{\le}0.35$, we find a possible PVB order, which shows a fast growing PVB decay length with increasing system width. For
0.22<J2/J1<0.25, both spin and dimer orders vanish in the thermodynamic limit, which is consistent with a possible spin liquid phase. We present calculations of the topological entanglement entropy, compare the DMRG results with the variational Monte Carlo, and discuss possible scenarios in the thermodynamic limit for this region.