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 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 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.
We study the zero-temperature phase diagram of the J 1 XXZ – J 2 XXZ Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour ( ) and next-nearest-neighbour ( J 2 >0) bonds. The two bonds have the same XXZ -type anisotropy in spin space. The effects on the quasiclassical Néel-ordered and collinear stripe-ordered states of varying the anisotropy parameter Δ are investigated using the coupled cluster method carried out up to high orders. By contrast with the case for spin- particles studied previously, no intermediate disordered phase between the Néel and collinear stripe phases, for any value of the frustration J 2 / J 1 , for either the z -aligned (Δ>1) or xy -planar-aligned (0≤Δ<1) states, is predicted here. The quantum phase transition is determined as first order for all values of J 2 / J 1 and Δ. The position of the phase boundary J 2 c (Δ) is determined accurately. It is observed to deviate most from its classical position (for all values of Δ>0) at the Heisenberg isotropic point (Δ = 1), where J 2 c (1) = 0.55 ± 0.01. By contrast, at the XY isotropic point (Δ = 0), we find J 2 c (0) = 0.50 ± 0.01. In the Ising limit ( ), as expected.
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 ${\ensuremath{\alpha}}^{{c}_{1}}({\ensuremath{\Delta}}^{c})={\ensuremath{\alpha}}^{{c}_{2}}({\ensuremath{\Delta}}^{c})$.
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.
We study the spin-1/2 and spin-1 J1-J2 Heisenberg antiferromagnets (HAFs) on an in–nite, anisotropic, two-dimensional triangular lattice, using the coupled cluster method. With respect to an underlying square–lattice geometry the model contains antiferromag- netic (J1 > 0) bonds between nearest neighbours and competing (J02 > 0) 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 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 and a set of de- coupled chains at the other, with the isotropic HAF on the triangular lattice in between at k = 1. For the spin-1/2 J1-J2 2 model, we a weakly order (or possibly second-order) quantum phase transition from a eel-ordered state to a helical state at critical point at and a second critical point at where a transition occurs between the helical state and a collinear stripe- ordered state. For the corresponding spin-1 model we an analogous transition of the second-order type at between states with and helical ordering, but we no evidence of a further transition in thiSocase to a stripe-ordered phase.