We study the J1-J1'-J2 quantum spin model on the two-dimensional square lattice using the coupled cluster method. We compare and contrast the influence of the interchain coupling J1' on the zero-temperature phase diagrams for the two spin values s = 1/2 and s = 1. Our most important result for the s = 1/2 case is the predicted existence of a quantum triple point (QTP) at (J1' ≈ 0.60 ± 0.03, J2 ≈ 0.33 ± 0.02) when J1 = 1. Below the QTP (J1'/J1 ≤ 0.60) we predict a second-order phase transition between the quasi-classical Neel and stripe-ordered phases, whereas the corresponding classical model, which contains only these two phases for all spin values s, yields a first-order transition. Above the QTP (J1'/J1 ≥ 0.60) an intermediate disordered phase emerges, which has no classical counterpart. By contrast, the situation for s = 1 is qualitatively different. Instead of a QTP where three phases co-exist, we now predict a quantum tricritical point at (J1' ≈ 0.66 ± 0.03, J2 ≈ 0.35 ± 0.02) when J1 = 1, where a line of second-order phase transitions between the quasi classical Neel and stripe-ordered phases (for J1'/J1 ≤ 0.66) meets a line of first-order phase transitions between the same two states (for J1'/J1 ≥ 0.66). Surprisingly, we find no evidence at all for any intermediate disordered phase in the s = 1 case.
We study the phase diagram of the isotropic J 1 – J 1 '– J 2 Heisenberg model for spin-1 particles on an anisotropic square lattice, using the coupled-cluster method. We find no evidence for an intermediate phase between the Néel and stripe states, as compared with all previous results for the corresponding spin-1/2 case. However, we find a quantum tricritical point at J 1 '/ J 1 ≈0.66±0.03, J 2 / J 1 ≈0.35±0.02, where a line of second-order phase transitions between the quasi-classical Néel and stripe-ordered phases (for J 1 '/ J 1 ≲0.66) meets a line of first-order phase transitions between the same two states (for J 1 '/ J 1 ≳0.66).
We study the zero-temperature phase diagram of the two-dimensional quantum
J1XXZ−−J2XXZ spin-1/2 anisotropic Heisenberg model on the square lattice. In particular, the effects of the anisotropy $\ensuremath{\Delta}$ on the
z-aligned N\'eel and (collinear) stripe states, as well as on the
xy-planar-aligned N\'eel and collinear stripe states, are examined. All four of these quasiclassical states are chosen in turn as model states, on top of which we systematically include the quantum correlations using a coupled cluster method analysis carried out to very high orders. We find strong evidence for two quantum triple points (QTPs) at $({\ensuremath{\Delta}}^{c}=\ensuremath{-}0.10\ifmmode\pm\else\textpm\fi{}0.15,\text{ }{J}_{2}^{c}/{J}_{1}=0.505\ifmmode\pm\else\textpm\fi{}0.015)$ and $({\ensuremath{\Delta}}^{c}=2.05\ifmmode\pm\else\textpm\fi{}0.15,\text{ }{J}_{2}^{c}/{J}_{1}=0.530\ifmmode\pm\else\textpm\fi{}0.015)$, between which an intermediate magnetically disordered phase emerges to separate the quasiclassical N\'eel and stripe collinear phases. Above the upper QTP $(\ensuremath{\Delta}\ensuremath{\gtrsim}2.0)$ we find a direct first-order phase transition between the N\'eel and stripe phases, exactly as for the classical case. The
z-aligned and
xy-planar-aligned phases meet precisely at $\ensuremath{\Delta}=1$, also as for the classical case. For all values of the anisotropy parameter between those of the two QTPs there exists a narrow range of values of
J2/J1, ${\ensuremath{\alpha}}^{{c}_{1}}(\ensuremath{\Delta})<{J}_{2}/{J}_{1}<{\ensuremath{\alpha}}^{{c}_{2}}(\ensuremath{\Delta})$, centered near the point of maximum classical frustration,
J2/J1=21, for which the intermediate phase exists. This range is widest precisely at the isotropic point, $\ensuremath{\Delta}=1$, where ${\ensuremath{\alpha}}^{{c}_{1}}(1)=0.44\ifmmode\pm\else\textpm\fi{}0.01$ and ${\ensuremath{\alpha}}^{{c}_{2}}(1)=0.59\ifmmode\pm\else\textpm\fi{}0.01$. The two QTPs are characterized by values $\ensuremath{\Delta}={\ensuremath{\Delta}}^{c}$ at which ${\ensuremath{\alpha}}^{{c}_{1}}({\ensuremath{\Delta}}^{c})={\ensuremath{\alpha}}^{{c}_{2}}({\ensuremath{\Delta}}^{c})$.
Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half (
s=21)
J1-
J2 Heisenberg model on a cross-striped square lattice. Each site of the square lattice has four nearest-neighbor exchange bonds of strength
J1 and two next-nearest-neighbor (diagonal) bonds of strength
J2. The
J2 bonds are arranged so that the basic square plaquettes in alternating columns have either both or no
J2 bonds included. The classical ($s\ensuremath{\rightarrow}\ensuremath{\infty}$) version of the model has four collinear phases when
J1 and
J2 can take either sign. Three phases are antiferromagnetic (AFM), showing so-called N\'eel, double N\'eel, and double columnar striped order, respectively, while the fourth is ferromagnetic. For the quantum
s=21 model we use the three classical AFM phases as CCM reference states, on top of which the multispin-flip configurations arising from quantum fluctuations are incorporated in a systematic truncation hierarchy. Calculations of the corresponding GS energy, magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order are thus carried out numerically to high orders of approximation and then extrapolated to the (exact) physical limit. We find that the
s=21 model has five phases, which correspond to the four classical phases plus a new quantum phase with plaquette VBC order. The positions of the five quantum critical points are determined with high accuracy. While all four phase transitions in the classical model are first order, we find strong evidence that three of the five quantum phase transitions in the
s=21 model are of continuous deconfined type.
We study the phase diagram of the two-dimensional (2D) J 1 – J 1 '– J 2 spin-1/2 Heisenberg model by means of the coupled cluster method. The effect of the coupling J 1 ' on the Néel and stripe states is investigated. We find that the quantum critical points for the Néel and stripe phases increase as the coupling strength J 1 ' is increased, and an intermediate phase emerges above the region at J 1 '≈0.6 when J 1 = 1. We find indications for a quantum triple point at J 1 '≈0.60 ± 0.03, J 2 ≈0.33 ± 0.02 for J 1 = 1.
Using the coupled cluster method for high orders of approximation and complementary exact diagonalization studies we investigate the ground state properties of the spin-1/2
J1−−J2 frustrated Heisenberg antiferromagnet on the square lattice. We have calculated the ground state energy, the magnetic order parameter, the spin stiffness, and several generalized susceptibilities to probe magnetically disordered quantum valence-bond phases. We have found that the quantum critical points for both the N\'eel and collinear orders are ${J}_{2}^{c1}\ensuremath{\approx}(0.44\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$ and ${J}_{2}^{c2}\ensuremath{\approx}(0.59\ifmmode\pm\else\textpm\fi{}0.01){J}_{1}$, respectively, which are in good agreement with the results obtained by other approximations. In contrast to the recent study by [Sirker et al. Phys. Rev. B 73, 184420 (2006)], our data do not provide evidence for the transition from the N\'eel to the valence-bond solid state to be first order. Moreover, our results are in favor of the deconfinement scenario for that phase transition. We also discuss the nature of the magnetically disordered quantum phase.
We study the spin-1/2 and spin-1 [Formula: see text] Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice, using the coupled cluster method. With respect to an underlying square-lattice geometry the model contains antiferromagnetic (J1 > 0) bonds between nearest neighbours and competing [Formula: see text] bonds between next-nearest-neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry the model has two sorts of nearest-neighbour bonds, with [Formula: see text] bonds along parallel chains and with J1 bonds providing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one extreme (κ = 0) and a set of decoupled chains at the other (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For the spin-1/2 [Formula: see text] model, we find a weakly first-order (or possibly second-order) quantum phase transition from a Néel-ordered state to a helical state at a first critical point at κc1 = 0.80 ± 0.01, and a second critical point at κc2 = 1.8 ± 0.4 where a first-order transition occurs between the helical state and a collinear stripe-ordered state. For the corresponding spin-1 model we find an analogous transition of the second-order type at κc1 = 0.62 ± 0.01 between states with Néel and helical ordering, but we find no evidence of a further transition in this case to a stripe-ordered phase.