裁剪零温张量网络实现量子多体热力学的高效模拟
Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network
摘要：
数值退火和重整化群已经为研究强关联系统的热力学问题提供了多种成功的方法，而微扰理论和膨胀理论都不能解决这些问题。由于降低温度的过程通常以不同的方式涉及，这些方法在低温下通常变得不那么有效或准确。在这项工作中，我们建议访问有限温度的性质，从张量网络（TN）表示零温度配分函数。我们建议从这样一个无限大小的TN中“裁剪”出一个有限的部分，并“缝合”它，使其沿时间-时间方向具有周期性边界条件。我们称这种方法为TN剪裁。通过微调过程实现了卓越的精度，超过了以前的方法，包括线性化张量重整化群[Phys. Rev. Lett. 106，127202（2011）]、连续矩阵乘积算子[Phys.Rev.Lett. 125，170604（2020）]等。证明了高效率，其中时间成本几乎与目标温度（包括极低温度）无关。这个想法可以推广到更高维的玻色子和费米子系统。
英文摘要：
Numerical annealing and renormalization group have conceived various successful approaches to study the thermodynamics of strongly-correlated systems where perturbation or expansion theories fail to work. As the process of lowering the temperatures is usually involved in different manners, these approaches in general become much less efficient or accurate at the low temperatures. In this work, we propose to access the finite-temperature properties from the tensor network (TN) representing the zero-temperature partition function. We propose to "scissor" a finite part from such an infinite-size TN, and "stitch" it to possess the periodic boundary condition along the imaginary-time direction. We dub this approach as TN tailoring. Exceptional accuracy is achieved with a fine-tune process, surpassing the previous methods including the linearized tensor renormalization group [Phys. Rev. Lett. 106, 127202 (2011)], continuous matrix product operator [Phys. Rev. Lett. 125, 170604 (2020)], and etc. High efficiency is demonstrated, where the time cost is nearly independent of the target temperature including the extremely-low temperatures. The proposed idea can be extended to higher-dimensional systems of bosons and fermions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
