Abstract
The zero-temperature ground-state (GS) properties and phase diagram of a frustrated spin-1 J1-J2 Heisenberg model on the checkerboard square lattice are studied, using the coupled cluster method. We consider the case where the nearest-neighbour exchange bonds have strength J1 > 0 and the next-nearest-neighbour exchange bonds present (viz., in the checkerboard pattern of the planar pyrochlore) have strength J2 = κJ1 > 0. We find significant differences from both the spin-1/2 and classical versions of the model. We find that the spin-1 model has a first phase transition at κC1 ≈ 1.00 ± 0.01 (as does the classical model at κcl = 1) between two antiferromagnetic phases, viz., a quasiclassical Néel phase (for κ < κC1) and one of the infinitely degenerate family of quasiclassical phases (for k > κC1) that exists in the classical model for κ > κc1, which is now chosen by the order by disorder mechanism as (probably) the "doubled Néel" (or Néel*) state. By contrast, none of this family survives quantum fluctuations to form a stable GS phase in the spin-1/2 case. We also find evidence for a second quantum critical point at κC2 ≈ 2.0 ± 0.5 in the spin-1 model, such that for κ > κC2 the quasiclassical (Néel*) ordering melts and a nonclassical phase appears, which, on the basis of preliminary evidence, appears unlikely to have crossed-dimer valence-bond crystalline (CDVBC) ordering, as in the spin-1/2 case. Unlike in the spin-1/2 case, where the Néel and CDVBC phases are separated by a phase with plaquette valence-bond crystalline (PVBC) ordering, we find very preliminary evidence for such a PVBC state in the spin-1 model for all κ > κC2.
Highlights
Low-dimensional spin-lattice models of magnetic systems, those pertaining to frustrated Heisenberg antiferromagnets (HAFMs) with competing interactions, have been extensively studied from both the theoretical and experimental viewpoints in recent years. such spin-lattice models are themselves conceptually simple and easy to write down, these strongly correlated systems often exhibit rich and interesting zero-temperature (T = 0)ground-state (GS) phase diagrams as the interaction coupling strengths are varied, due to the strong interplay between quantum fluctuations and frustration
quantum Monte Carlo (QMC) methods suffer in such cases from the infamous “minus-sign problem,” while exact diagonalization (ED) methods are often restricted to too small lattices to be able to sample with sufficient accuracy the details of the often very subtle ordering that is present, even when state-of-the-art calculations are performed with the largest computational resources available. While both QMC and ED calculations are performed on lattices with a finite number N of spins, and require finite-size scaling to obtain the N → ∞ limit required, the CCM, as we described below, is a size-extensive method that automatically works in the thermodynamic limit from the outset, at every level of approximation
We present our CCM results for the spin-1 J1–J2 model on the checkerboard lattice, using both the Neel and Neel∗ states shown in Fig. 1 as model states, and employing the SUBn–n truncation scheme with n ≤ 8
Summary
We present our CCM results for the spin-1 J1–J2 model on the checkerboard lattice, using both the Neel and Neel∗ states shown in Fig. 1 as model states, and employing the SUBn–n truncation scheme with n ≤ 8.
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