基于时间演化块消减的张量网络蒙特卡洛方法
Tensor-network Monte Carlo approach based on time-evolving block decimation
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中文总结 AI 辅助
提出张量网络蒙特卡洛方法，通过采样避免截断误差，在有限键维下实现无偏期望值估计，并应用于哈密顿量与Floquet动力学，优于同键维的TEBD方法。
中文摘要 AI 辅助
我们提出了一种张量网络蒙特卡洛（TNMC）方法，用于幺正演化，该方法遵循时间演化块消减（TEBD）算法的压缩序列。在TNMC方法中，所获得的结果包含可评估的统计误差而非截断误差，这与基于奇异值分解的普通方法（如TEBD算法）不同。因此，即使在有限键维下，也能在统计误差范围内估计无偏的期望值。由于在幺正演化模拟中引入了采样方案，所提出的蒙特卡洛方案可能面临符号问题。我们观察到，增加键维可以缓解符号问题。我们将所提出的TNMC方法应用于哈密顿量和Floquet动力学。数值实验表明，即使在与相同键维的TEBD方法无法准确估计可观测量期望值的情况下，TNMC方法也能准确估计。所提出的方法可为改进幺正演化的经典可模拟性提供新方向。
英文摘要
We propose a tensor-network Monte Carlo (TNMC) approach for unitary evolution following the compression sequence of the time-evolving block decimation (TEBD) algorithm. In the TNMC approach, the obtained results contain evaluable statistical errors rather than truncation errors, unlike ordinary singular-value-decomposition-based methods such as the TEBD algorithm. Consequently, one can estimate unbiased expectation values within statistical errors even with a finite bond dimension. Since the sampling scheme is introduced in the simulations of unitary evolution, the proposed Monte Carlo scheme may suffer from a sign problem. We observe that the sign problem can be mitigated by increasing the bond dimension. We apply the proposed TNMC approach to the Hamiltonian and the Floquet dynamics. Numerical experiments show that the TNMC approach can estimate accurate expectation values of observables even when the TEBD method with the same bond dimension cannot. The proposed approach can be a new direction for improving the classical simulatability of unitary evolution.
发表机构
- The University of Tokyo（东京大学）
- Institute for Physics of Intelligence, The University of Tokyo（东京大学物理智能研究所）
- Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
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