We address the ground-state properties of the long-standing and much-studied three-dimensional quantum spin liquid candidate, the S=1/2 pyrochlore Heisenberg antiferromagnet. By using SU(2) density-matrix renormalization group (DMRG), we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground-state energy, E_{0}/N_{sites}=-0.490(6)J, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.
We investigate the ground-state properties of the nearest-neighbor
S=1 pyrochlore Heisenberg antiferromagnet using two complementary numerical methods, the density-matrix renormalization group (DMRG) and pseudofermion functional renormalization group (PFFRG). Within DMRG, we are able to reliably study clusters with up to 48 spins by keeping 20 000 SU(2) states. The investigated 32-site and 48-site clusters both show indications of a robust
C3 rotation symmetry breaking of the ground-state spin correlations and the 48-site cluster additionally features inversion symmetry breaking. Our PFFRG analysis of various symmetry-breaking perturbations corroborates the findings of either
C3 or a combined
C3/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the
S=1/2 system.
We investigate the ground-state properties of the nearest-neighbor S=1 pyrochlore Heisenberg antiferromagnet using two complementary numerical methods, the density-matrix renormalization group (DMRG) and pseudofermion functional renormalization group (PFFRG). Within DMRG, we are able to reliably study clusters with up to 48 spins by keeping 20 000 SU(2) states. The investigated 32-site and 48-site clusters both show indications of a robust C3 rotation symmetry breaking of the ground-state spin correlations and the 48-site cluster additionally features inversion symmetry breaking. Our PFFRG analysis of various symmetry-breaking perturbations corroborates the findings of either C3 or a combined C3/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the S=1/2 system.
We investigate the ground-state properties of the spin-
1/2 pyrochlore Heisenberg antiferromagnet using pseudofermion functional renormalization group techniques. The first part of our analysis is based on an enhanced parton mean-field approach, which takes into account fluctuation effects from renormalized vertex functions. Our implementation of this technique extends earlier approaches and resolves technical difficulties associated with a diagrammatic overcounting. Using various parton ans\"atze for quantum spin liquids, dimerized and nematic states our results indicate a tendency for lattice symmetry breaking in the ground state. While overall quantum spin liquids seem unfavorable in this system, the recently proposed monopole state still shows the strongest support among all spin liquid ans\"atze that we have tested, which is further confirmed by our complementary variational Monte Carlo calculations. In the second part of our investigation, we probe lattice symmetry breaking more directly by applying the pseudofermion functional renormalization group to perturbed systems. Our results from this technique confirm that the system's ground state either exhibits broken
C3 rotation symmetry, or a combination of inversion and
C3 symmetry breaking.
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 resonating-valence-bond-like, manyvariable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4 × 4 3 and 4 × 3 3 spins, respectively.We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit.We consider the ðλ; j 2 =j 1 Þ parameter space, with j 2 , j 1 being nearest and next-to-nearest neighbor interactions and λ the XXZ interaction anisotropy.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 a dimer order with 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.
We use a combination of three computational methods to investigate the notoriously difficult frustrated three-dimensional pyrochlore
S=21 quantum antiferromagnet, at finite temperature
T: canonical typicality for a finite cluster of $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ unit cells (i.e., 32 sites), a finite-
T matrix product state method on a larger cluster with 48 sites, and the numerical linked cluster expansion (NLCE) using clusters up to 25 lattice sites, including nontrivial hexagonal and octagonal loops. We calculate thermodynamic properties (energy, specific heat capacity, entropy, susceptibility, magnetization) and the static structure factor. We find a pronounced maximum in the specific heat at
T=0.57J, which is stable across finite size clusters and converged in the series expansion. At $T\ensuremath{\approx}0.25J$ (the limit of convergence of our method), the residual entropy per spin is
0.47kBln2, which is relatively large compared to other frustrated models at this temperature. We also observe a nonmonotonic dependence on
T of the magnetization at low magnetic fields, reflecting the dominantly nonmagnetic character of the low-energy states. A detailed comparison of our results to measurements for the
S=1 material
NaCaNi2F7 yields a rough agreement of the functional form of the specific heat maximum, which in turn differs from the sharper maximum of the heat capacity of the spin ice material
Dy2Ti2O7.
We examine the perennial quantum spin liquid candidate
S=21 Heisenberg antiferromagnet on the kagome lattice. Our paper is based on achieving Lanczos diagonalization of the Hamiltonian on a 48 site cluster in sectors with dimensions as large as $5\ifmmode\times\else\texttimes\fi{}{10}^{11}$. The results reveal intricate structures in the low-lying energy spectrum. These structures by no means unambiguously support a
Z2 spin liquid ground state, but instead appear compatible with several scenarios, including fourfold topological degeneracy, inversion symmetry breaking, and a combination thereof. We discuss finite-size effects, such as the apparent absence of the eigenstate thermalization hypothesis, and note that, while considerably reduced, some are still present for the largest cluster. Finally, we observe that an XXZ model in the Ising limit reproduces remarkably well the most striking features of finite-size spectra.