使用置信传播的DMRG
DMRG using Belief Propagation
- Technical University of Munich（慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究将置信传播（BP）与DMRG算法结合，扩展DMRG至高维及任意晶格，在横场伊辛模型上验证其可生成高保真基态，能量估计误差小，且随机晶格上保真度随横场增大而提高。
AI中文摘要：
张量网络作为模拟量子多体系统的强大工具已受到广泛关注，但其收缩是一大挑战，尤其在高度连接的网络中，内存需求过高且最优收缩顺序难以确定。置信传播（BP）算法作为精确收缩的替代方案被提出，因以与图无关的方式构建而具备高灵活性，但在存在环的情况下准确性会下降。本研究将BP与DMRG算法结合以求解基态问题，从而将DMRG扩展至更高维度和任意晶格。我们在2×2六角晶格的横场伊辛模型（TFI）上验证了BP-DMRG的可行性，发现其生成的态与真实基态的保真度在0.9至0.99之间，能量估计的相对误差在10⁻²至10⁻³之间。此外，BP-DMRG可在随机生成的晶格上找到基态，且保真度随横场增大而提高。最后，我们讨论了使用置信传播时遇到的局限性，强调TFI张量网络算子在BP-DMRG的BP迭代过程中会导致更大误差。
英文摘要：
Tensor networks have attracted much attention as a powerful tool for modeling quantum many-body systems. Their contraction is a significant challenge, however, especially in highly connected networks, as memory requirements become prohibitive and the optimal contraction order is increasingly hard to find. The belief propagation (BP) algorithm has emerged as an alternative to exact contraction. Being formulated in a graph-agnostic way, it offers great flexibility, but its accuracy suffers in the presence of loops. In this work, we combine BP with the DMRG algorithm to solve ground-state problems, thereby extending DMRG to higher dimensions and arbitrary lattices. We demonstrate the viability of BP-DMRG on the transverse-field Ising model on a $2\times 2$ hexagonal lattice, finding that it produces states with a fidelity between $0.9$ and $0.99$ to the true ground state, and energy estimates with a relative error between $10^{-2}$ and $10^{-3}$. Additionally, BP-DMRG can find ground states on randomly generated lattices, with fidelity improving as the transverse field increases. We conclude with a discussion of the limitations we encounter when using belief propagation, highlighting that the TFI tensor network operators lead to larger errors during BP iterations in BP-DMRG.
