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arXiv:2110.08160 · Physical review. B./Physical review. B

Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective

Max Hering, Vincent Noculak, Francesco Ferrari, Yasir Iqbal, Johannes Reuther

Published Feb 24, 2022• 35 citations
arXivHTMLPDF

Abstract

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 ${C}_{3}$ rotation symmetry, or a combination of inversion and ${C}_{3}$ symmetry breaking.

DOI
10.1103/physrevb.105.054426

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We investigate the ground-state properties of the spin-1/21/21/2 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{C}_{3}C3​ rotation symmetry, or a combination of inversion and C3{C}_{3}C3​ symmetry breaking.
Enhanced symmetry-breaking tendencies in the S=1S=1S=1 pyrochlore antiferromagnet
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=1S=1S=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{C}_{3}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{C}_{3}C3​ or a combined C3{C}_{3}C3​/inversion symmetry breaking. Moreover, in both methods the symmetry-breaking tendencies appear to be more pronounced than in the S=1/2S=1/2S=1/2 system.
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 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.
Ground state of the SSS=1/2 pyrochlore Heisenberg antiferromagnet: A quantum spin liquid emergent from dimensional reduction
The quantum antiferromagnet on the pyrochlore lattice offers an archetypal frustrated system, which potentially realizes a quantum spin liquid characterized by the absence of standard spontaneous symmetry breaking even at zero temperature, unusually as an isotropic 3D system. Despite tremendous progress in the literature, however, the nature of the ground state of the fully quantum-mechanical spin Hamiltonian on the pyrochlore lattice still remains elusive. Here, we show that an unconventional type of quantum spin liquid is born out from the pyrochlore system after the self-organized dimensional reduction leading to confined states in 2D layers. This conclusion is obtained from state-of-the-art variational Monte Carlo (VMC) simulations at zero temperature. Quantum spin liquids triggered by the emergent dimensional reduction is an unexplored route of the spin-liquid formation. The dimensional reduction from 3D to 2D is a consequence of a conventional spontaneous symmetry breaking, while the resultant decoupling of layers enables the emergence of a 2D quantum spin liquid that is adiabatically disconnected from trivial product states and exhibits strong quantum entanglement. The stabilized quantum spin liquid exhibits an algebraic decay of correlations and vanishing excitation gap in the thermodynamic limit. The wave-function structure supports the fractionalization of the spin into spinons. This spin-liquid ground state persists in the presence of spin-orbit interactions, which expands the possibilities of realizing quantum spin liquids in real pyrochlore-structured materials.
Abstract We present a systematic classification and variational study of chiral quantum spin liquids on the pyrochlore lattice based on fermionic parton constructions. Focusing on chiral U ( 1 ) and Z 2 spin-liquid Ansätze , we characterize their symmetry properties, flux structures, and low-energy spinon spectra within a projective symmetry group framework, and incorporate gauge fluctuations through Gutzwiller-projected wave functions studied by variational Monte Carlo. From the equal-time spin structure factor, we develop correlation-based diagnostics that distinguish gauge-dominated Coulomb phases from states with substantial matter-field and short-range contributions. Distinct chiral flux sectors, though close in energy, exhibit markedly different degrees of emergent U ( 1 ) gauge-field dominance, reflected in the geometry and contrast of pinch-point singularities. Although these states are not competitive ground states of the nearest-neighbor Heisenberg model, they define a physically meaningful family of proximate chiral phases relevant to extended pyrochlore Hamiltonians.