The nature of the intermediate ground‐state phase in the spin‐1/2 frustrated square lattice model has long been debated. We investigate the phase diagram of this model using cluster density matrix embedding theory (CDMET). Two antiferromagnetic phases are directly identified from our analysis of the ground‐state wave function: the Néel antiferromagnetic phase for J 2 ≤ 0.45 and the stripe antiferromagnetic phase for J 2 ≥ 0.65. Although our analysis of the ground state finds no direct evidence of an internal phase transition within the intermediate phase, an examination of the first excited state reveals a continuous quantum phase transition therein, with a critical point at J 2 = 0.55 that separates the intermediate phase into a plaquette valence bond solid (PVBS) and a (P + C) valence bond solid (VBS).
The nature of the intermediate ground‐state phase in the spin‐1/2 frustrated square lattice model has long been debated. We investigate the phase diagram of this model using cluster density matrix embedding theory (CDMET). Two antiferromagnetic phases are directly identified from our analysis of the ground‐state wave function: the Néel antiferromagnetic phase for J 2 ≤ 0.45 and the stripe antiferromagnetic phase for J 2 ≥ 0.65. Although our analysis of the ground state finds no direct evidence of an internal phase transition within the intermediate phase, an examination of the first excited state reveals a continuous quantum phase transition therein, with a critical point at J 2 = 0.55 that separates the intermediate phase into a plaquette valence bond solid (PVBS) and a (P + C) valence bond solid (VBS).
The nature of the intermediate ground-state phase in the spin-1/2 frustrated square lattice model has long been debated. Using cluster density matrix embedding theory, we investigate the phase diagram of this model. The Neel phase is directly identified for J2<0.45 and the collinear phase for J2>0.65 based on the ground state. Although no direct evidence of an internal phase transition is found within the intermediate phase from the ground state, analysis of the first excited state wave function reveals a continuous quantum phase transition in this region, with a critical point at J2=0.55. This critical point divides the intermediate phase into PVBS and CVBS.
We perform an in-depth investigation of the phase diagram of the ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model on the square lattice. We take advantage of density matrix renormalization group and fully augmented matrix product states methods and reach unprecedented accuracy with large bond dimensions. We utilize excited-level crossing analysis to pinpoint the phase transition points. It was believed before that there exists a narrow spin liquid phase sandwiched by the N\'eel antiferromagnetic (AFM) and valence bond solid (VBS) phases. Through careful finite-size scaling of the level crossing points, we find a direct phase transition between the N\'eel AFM and VBS phases at J2/J1=0.535(3), suggesting the absence of an intermediate spin liquid phase. We also provide accurate results for ground-state energies for a variety of sizes, from which we find that the transition between the N\'eel AFM and VBS phases is continuous. These results indicate the existence of a deconfined quantum critical point at J2/J1=0.535(3) in the model. From the crossing of the first derivative of the energies with J2 for different sizes, we also determine the precise location of the first-order phase transition between the VBS and stripe AFM phases at J2/J1=0.610(5).
The ground-state (GS) phase diagram of the frustrated spin- s J 1 -J 2 -J 3 Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method implemented to high orders of approximation, for spin quantum numbers s = 1, 3/2, 2 , 5/2. The model has antiferromagnetic (AFM) nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour exchange couplings (with strength J 1 > 0, J 2 > 0 and J 3 > 0, respectively). We specifically study the case J 3 = J 2 = κJ 1 , in the range 0 < κ < 1 of the frustration parameter, which includes the point of maximum classical (s → ∞ ) frustration, viz., the classical critical point at κ cl = 1/2 , which separates the Neel phase for κ < κ cl and the collinear striped AFM phase for κ > κ cl . Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins s > 3/2 we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value κ c (s) which is slightly greater than κ c l [e.g., κ c (3/2) ≈ 0.53(1)] and which approaches it monotonically as s → ∞ . By contrast, for the case s = 1 the transition is split into two such that the stable GS phases are one with Néel AFM order for κ < κ c1 = 0.485(5) and one with striped AFM order for κ > κ c2 = 0.528(5), just as in the case s = 1/2 (for which κ c1 ≈ 0.47 and κ c2 ≈ 0.60). For both the s = 1/2 and s = 1 models the transition at κ c2 appears to be of first-order type, while that at κ c1 appears to be continuous. However, whereas in the s = 1/2 case the intermediate phase appears to have PVBC order over the entire range κ c1 < κ < κ c2 , in the s = 1 case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.
We study the phase diagram and the dynamical spin structure factor of the spin-1/2 J1−−J3 Heisenberg model on the square lattice using density matrix renormalization group, exact diagonalization (ED), and cluster perturbation theory (CPT). By extrapolating the order parameters and studying the level crossings of the low-lying energy and entanglement spectra, we obtain the phase diagram of this model and identify a narrow region of quantum spin liquid (QSL) phase followed by a plaquette valence-bond solid (PVBS) state in the intermediate region, whose nature has been controversial for many years. More importantly, we use CPT and ED to study the dynamical spin structure factor in the QSL and the PVBS phase. In the QSL phase, the high-energy magnon mode completely turns into some dispersive weak excitations around the X and M points. For the PVBS phase, the low-energy spectrum is characterized by a gapped triplet excitation, and at the high energy, we find another branch of dispersive excitation with broad continua, which is unlike the plaquette phase in the $2\ifmmode\times\else\texttimes\fi{}2$ checkerboard model. In the latter case, the second branch of excitation is nearly flat due to the weak effective interactions between the local excitations of the plaquettes. And in the J1−−J3 Heisenberg model, the uniform interactions and the spontaneously translational symmetry breaking of the PVBS phase make the difference in the excitation spectra.
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.
We study the N\'eel to fourfold columnar valence bond solid (cVBS) quantum phase transition in a sign-free S=1 square-lattice model. This is the same kind of transition that for S=1/2 has been argued to realize the prototypical deconfined critical point. Extensive numerical simulations of the square-lattice S=1/2 N\'eel-VBS transition have found consistency with the deconfined critical point scenario with no direct evidence for first-order behavior. In contrast to the S=1/2 case, in our quantum Monte Carlo simulations for the S=1 model, we present unambiguous evidence for a direct conventional first-order quantum phase transition. Classic signs of a first-order transition demonstrating coexistence including double-peaked histograms and switching behavior are observed. The sharp contrast from the S=1/2 case is remarkable; we hypothesize that this is a striking demonstration of the role of the size of the quantum spin in the phase diagram of two-dimensional lattice models.