Ground State Calculations Achieve 3 Orders of Magnitude Speedup with Tensor Networks
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Determining the ground state of complex two-dimensional systems presents a significant challenge in physics, demanding increasingly powerful computational methods. Hongyu Chen from Renmin University of China, alongside Yangfeng Fu and Weiqiang Yu, now present a novel single-layer tensor network framework that dramatically reduces the computational cost of these calculations. This approach combines established tensor network techniques with automatic differentiation, achieving a three-order-of-magnitude reduction in required bond dimension and enabling highly efficient ground-state calculations for complex spin models.
The team demonstrates the framework’s capability through simulations of the antiferromagnetic Heisenberg model and the frustrated Shastry-Sutherland model, confirming known ground states and even verifying the existence of a specific valence bond solid phase, paving the way for large-scale tensor network calculations of previously intractable two-dimensional systems. The capability of this framework is demonstrated through investigations of two quantum spin models: the antiferromagnetic Heisenberg model on a square lattice and the frustrated Shastry-Sutherland model. Even without employing GPU acceleration or symmetry implementation, the team achieved a bond dimension of 9 and obtained accurate ground-state energy and consistent order parameters, confirming results from prior studies. These findings demonstrate the effectiveness of the method for tackling complex quantum systems and provide a foundation for future investigations into strongly correlated materials. Tensor Networks and Automatic Differentiation for Quantum Systems This research develops and applies advanced numerical methods, specifically tensor network states and machine learning techniques like automatic differentiation, to solve problems in condensed matter physics. The primary goal is to accurately simulate the behavior of strongly correlated quantum systems, notoriously difficult to model with traditional computational approaches. These systems exhibit complex phenomena such as high-temperature superconductivity and magnetism. The simulation relies on tensor network states, a powerful way to represent the quantum state of many-body systems efficiently, avoiding the exponential growth of computational resources. Automatic differentiation, implemented using frameworks like PyTorch and Zygote, allows for the efficient calculation of derivatives, essential for optimization algorithms that find the ground state. This integration demonstrates a move towards combining quantum simulation with machine learning techniques. The methods are applied to strongly correlated quantum systems exhibiting complex phases of matter, potentially including systems relevant to high-temperature superconductivity and magnetism. By combining the power of tensor network states with the efficiency of automatic differentiation and machine learning, the authors have developed new tools for studying complex quantum systems, potentially accelerating the discovery of new materials and deepening our understanding of fundamental physics.
Efficient Ground State Calculations with Tensor Networks This work presents a new computational framework for determining the ground state properties of complex two-dimensional quantum systems, achieving significant reductions in computational cost. By combining a nested tensor network method with automatic differentiation, scientists have developed an approach that dramatically improves efficiency, enabling highly accurate results with substantially reduced computational resources.
The team demonstrated the capabilities of this framework using two distinct spin models: the antiferromagnetic Heisenberg model on a square lattice and the frustrated Shastry-Sutherland model. Experiments achieved a bond dimension of 9, even without utilizing GPU acceleration or symmetry implementation, and obtained ground-state energies and order parameters consistent with prior studies. Crucially, the research confirms the existence of an intermediate empty-plaquette valence bond solid ground state within the Shastry-Sutherland model, providing further insight into its complex quantum behavior. The method’s efficiency stems from a novel approach to calculating gradients, utilizing automatic differentiation to bypass the need to store large intermediate tensors in memory, a common bottleneck in tensor network calculations. This breakthrough delivers a three-order-of-magnitude reduction in computational cost related to bond dimension, allowing for calculations previously inaccessible due to resource limitations.
The team investigated the convergence of the method and identified potential avenues for future improvements, paving the way for large-scale tensor network calculations of two-dimensional systems and advancing our understanding of quantum materials.
Efficient Ground State Calculations with Tensor Networks This work presents a new single-layer tensor network framework for determining the ground states of two-dimensional lattice models, significantly improving computational efficiency. By combining a nested tensor network method with automatic differentiation, researchers achieved a reduction in computational cost of three orders of magnitude compared to traditional calculations, enabling highly accurate ground-state calculations with a bond dimension of nine. The framework’s validity was demonstrated through detailed analysis of the antiferromagnetic Heisenberg model on a square lattice and the frustrated Shastry-Sutherland model. Notably, the team confirmed the existence of an intermediate empty-plaquette valence bond solid ground state within the Shastry-Sutherland model, corroborating previous findings and strengthening understanding of this complex system. The researchers systematically analysed the convergence of their method, observing nearly complete convergence even at the largest bond dimension tested. This achievement paves the way for large-scale tensor network calculations applicable to more complex quantum systems, including investigations into superconductivity and excited state dynamics. The authors acknowledge that further improvements are possible, such as incorporating spin symmetry and employing techniques like checkpointing or fixed-point methods to reduce computational demands. 👉 More information 🗞 A single-layer framework of variational tensor network states 🧠 ArXiv: https://arxiv.org/abs/2512.14414 Tags: