论文标题
通过调整零温度张量网络对量子多体热力学的有效仿真
Efficient Simulation of Quantum Many-body Thermodynamics by Tailoring Zero-temperature Tensor Network
论文作者
论文摘要
数值退火和重新归一化组已经构想了各种成功的方法来研究扰动或扩展理论无法正常工作的强相关系统的热力学。由于降低温度的过程通常涉及不同的举止，因此在低温下，这些方法的效率降低或准确。在这项工作中，我们建议从代表零温度分区函数的张量网络（TN）访问有限温度属性。我们建议从这种无限大小的TN中“剪裁”一个有限的部分，并“针迹”它具有沿虚构时间方向的周期性边界条件。我们将这种方法称为TN裁缝。通过微调工艺可以实现出色的精度，超过了先前的方法，包括线性化张量重归其化组[Phys。莱特牧师。 106，127202（2011）]，连续矩阵产品运算符[Phys。莱特牧师。 125，170604（2020）]等。证明了高效率，其中时间成本几乎独立于目标温度，包括极低的温度。拟议的想法可以扩展到玻色子和费米子的高维系统。
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.
