Differentiable programming tensor networks for Kitaev magnets

Abstract

We present a general computational framework to investigate ground state properties of quantum spin models on infinite two-dimensional lattices using automatic differentiation-based gradient optimization of infinite projected entangled-pair states. The approach exploits the variational uniform matrix product states to contract infinite tensor networks with unit-cell structure and incorporates automatic differentiation to optimize the local tensors. We applied this framework to the Kitaev-type model, which involves complex interactions and competing ground states. To evaluate the accuracy of this method, we compared the results with exact solutions for the Kitaev model and found that it has a better agreement for various observables compared to previous tensor network calculations based on imaginary-time projection. Additionally, by finding out the ground state with lower variational energy compared to previous studies, we provided convincing evidence for the existence of nematic paramagnetic phases and 18-site configuration in the phase diagram of the $K$-$\Gamma$ model. Furthermore, in the case of the realistic $K$-$J$-$\Gamma$-${\Gamma }^{\prime }$ model for the Kitaev material $\alpha$-RuCl${}_3$, we discovered a non-colinear zigzag ground state. Lastly, we also find that the strength of the critical out-of-plane magnetic field that suppresses such a zigzag state has a lower transition field value than the previous finite-cylinder calculations. The framework is versatile and will be useful for a quick scan of phase diagrams for a broad class of quantum spin models.

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Cited by in corpus (9)

• Fermionic tensor network methods
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Accelerating two-dimensional tensor network optimization by preconditioning
• Efficient iPEPS Simulation on the Honeycomb Lattice via QR-based CTMRG
• Dynamic Hologram Generation with Automatic Differentiation
• Accelerating two-dimensional tensor network contractions using QR decompositions
• Variational optimization of projected entangled-pair states on the triangular lattice