Abstract
The spin-1/2 Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4\times 4^3$ and $4 \times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin-liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.
Highlights
Featureless ground states of interacting quantum spins with exotic properties and emergent excitations are highly sought after
We present our results in the following order: First, we demonstrate that the variational energies we obtain compare favorably to the previous studies; we show finitesize extrapolations based on computations with system sizes beyond those available in the literature
We have studied the physical observables along the phase transition between the putative quantum spin liquids (QSL) phase at j2=j1 1⁄4 0 and the magnetically ordered k 1⁄4 0 phase at large j2=j1
Summary
Featureless ground states of interacting quantum spins with exotic properties and emergent excitations are highly sought after. A QSL phase, if present, is expected to be close in parameter space to several symmetry-breaking ordered phases [28,29,30,31,32] These ordered phases can be induced by including next-to-nearest neighbor couplings [22,28] or large transverse exchange interactions, with the latter stabilizing spin-nematic order [8,9,23,24]. We assess whether the spin-1=2 pyrochlore quantum antiferromagnet hosts a QSL or a symmetrybroken ground state [38] in the vicinity of the SUð2Þsymmetric point and further identify the adjacent phases For this we use state-of-the-art variational Monte Carlo (VMC) methods. III, we discuss our results, starting with a validation of the method by combining results from ED with the two variational approaches and a characterization of the magnetically ordered phase This is followed by a thorough analysis of the symmetry-breaking signatures in the nonmagnetic phase.
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