Gradient optimization of finite projected entangled pair states

Abstract

The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond dimension $D$, in a practical application PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, the frustrated systems. The optimization of the ground state using time evolution method with simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that combining the time evolution method with simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel computing, we can study the quantum systems with larger bond dimensions up to $D$=10 without resorting to any symmetry. Benchmark tests of the method on the $J_1$-$J_2$ model give impressive accuracy compared with exact results.

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• Quantum critical phase with infinite projected entangled paired states
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• The emergence of gapless quantum spin liquid from deconfined quantum critical point
• Optimized contraction scheme for tensor-network states
• Multigrid Renormalization
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• From Tensor Network Quantum States to Tensorial Recurrent Neural Networks
• Population Control Bias and Importance Sampling in Full Configuration Interaction Quantum Monte Carlo
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• Accurate Simulation of the Hubbard Model with Finite Fermionic Projected Entangled Pair States
• Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
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• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
• Matrix Product States with Backflow correlations
• Efficient calculation of three-dimensional tensor networks
• Tensor Network Computations That Capture Strict Variationality, Volume Law Behavior, and the Efficient Representation of Neural Network States
• Entanglement entropy scaling of noisy random quantum circuits in two dimensions
• Combination of Tensor Network States and Green's function Monte Carlo
• Projected entangled pair states study of anisotropic-exchange magnets on triangular lattice
• Discrete lattice symmetry breaking in a two-dimensional frustrated spin-1 Heisenberg model
• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• TNSPackage: A Fortran2003 library designed for tensor network state methods
• Efficient optimization and conceptual barriers in variational finite Projected Entangled-Pair States
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Simulation of the Ring-exchange Models with Projected Entangled Pair States
• Neuralized Fermionic Tensor Networks for Quantum Many-Body Systems
• Solving Sharp Bounded-error Quantum Polynomial Time Problem by Evolution methods