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Quantum Phase Transitions of a Square Lattice Heisenberg Antiferromagnet with Two Kinds of Nearest-Neighbour Bonds: A High-Order Coupled Cluster Treatment

S.E. Krueger, Johannes Richter, J. Schulenburg, R. F. Bishop, DAMIAN J. J. FARNELL

Published Jan 1, 2000• 0 citations
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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.

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We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spin-half Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbor exchange bonds [J>0[J>0[J>0 (antiferromagnetic) and $\ensuremath{-}\ensuremath{\infty}<{J}^{\ensuremath{'}}<\ensuremath{\infty}]$ using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a N\'eel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with N\'eel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants ${J}^{\ensuremath{'}}>0.$ For frustrating ferromagnetic couplings ${J}^{\ensuremath{'}}<0$ we find indications that quantum fluctuations favor a first-order phase transition from the N\'eel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of ${J}^{\ensuremath{'}}=0,$ which is equivalent to the honeycomb lattice, is treated more closely.
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.
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.