Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice

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.

arXiv comment9 pages, 5 figures

References in corpus (65)

• The density-matrix renormalization group
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Quantum Spin Liquids
• Machine learning phases of matter
• Many-body quantum state tomography with neural networks
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Emergent excitations in a geometrically frustrated magnet
• Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Quantum Excitations in Quantum Spin Ice
• Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid
• Coulombic Quantum Liquids in Spin-1/2 Pyrochlores
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Green Function Monte Carlo with Stochastic Reconfiguration
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Correlated geminal wave function for molecules: an efficient resonating valence bond approach
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Singlet Excitations in Pyrochlore: A Study of Quantum Frustration
• Quantum Neural Network States: A Brief Review of Methods and Applications
• Origin of high-Tc superconductivity in doped Hubbard models and their extensions: Roles of uniform charge fluctuations
• mVMC - Open-source software for many-variable variational Monte Carlo method
• Neural Gutzwiller-projected variational wave functions
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• Neural network wave functions and the sign problem
• Antiferromagnetic Quantum Spins on the Pyrochlore Lattice
• Interaction driven phases in the honeycomb lattice from exact diagonalization
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• From Spin Glass to Quantum Spin Liquid Ground States in Molybdate Pyrochlores
• Partial order from disorder in a classical pyrochlore antiferromagnet
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice
• Frustrated Heisenberg antiferromagnet on a pyrochlore lattice
• Signatures of a gearwheel quantum spin liquid in a spin-$\frac{1}{2}$ pyrochlore molybdate Heisenberg antiferromagnet
• Monopole Flux State on the Pyrochlore Lattice
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Quantum spin ice on the breathing pyrochlore lattice
• Cubic and non-cubic multiple-q states in the Heisenberg antiferromagnet on the pyrochlore lattice
• The Spectral Periodicity of Spinon Continuum in Quantum Spin Ice
• Topological magnons with nodal-line and triple-point degeneracies: Implications for thermal Hall effect in pyrochlore iridates
• Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics
• Identification of an RVB liquid phase in a quantum dimer model with competing kinetic terms
• Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculations
• Corrections to Pauling residual entropy and single tetrahedron based approximations for the pyrochlore lattice Ising antiferromagnet
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Pseudo-Goldstone magnons in the frustrated S=3/2 Heisenberg helimagnet ZnCr2Se4 with a pyrochlore magnetic sublattice
• Quantum dimer models and effective Hamiltonians on the pyrochlore lattice
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• Hubbard Model on the Pyrochlore Lattice: a 3D Quantum Spin Liquid
• Unitary long-time evolution with quantum renormalization groups and artificial neural networks
• Novel ordering of the pyrochlore Heisenberg antiferromagnet with the ferromagnetic next-nearest-neighbor interaction
• lattice-symmetries: A package for working with quantum many-body bases
• Variational classical networks for dynamics in interacting quantum matter
• The spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalisation study
• Variational wave functions for the spin-Peierls transition in the Su-Schrieffer-Heeger model with quantum phonons

Cited by in corpus (3)

• Ab-initio quantum chemistry with neural-network wavefunctions
• Empowering deep neural quantum states through efficient optimization
• Many-body quantum sign structures as non-glassy Ising models