Locally accurate matrix product approximation to thermal states  

吉布斯态的局部精确的矩阵乘积近似

作　　者：Yichen Huang 黄溢辰(Center for Theoretical Physics,Massachusetts Institute of Technology,Cambridge,Massachusetts 02139,USA)

机构地区：[1]Center for Theoretical Physics,Massachusetts Institute of Technology,Cambridge,Massachusetts 02139,USA

出　　处：《Science Bulletin》2021年第24期2456-2457,M0003,共3页科学通报（英文版）

基　　金：supported by the National Science Foundation Grant PHY-1818914;a Samsung Advanced Institute of Technology Global Research Partnership。

摘　　要：Classical simulation of quantum many-body systems is a fundamental problem in computational physics.One difficulty is that a generic many-body state cannot even be represented in polynomial space because the dimension of the Hilbert space grows exponentially with the system size.Fortunately,many physically interesting states are non-generic and structured.It may be possible to avoid the‘‘curse of dimensionality”by exploiting their structure.量子多体系统的数值模拟是计算物理学中的一个基本问题.在具有短程相互作用的一维量子系统中,一系列领先的数值方法基于矩阵乘积态(matrix product state),其连接维数(bond dimension)决定了这些方法所需的计算资源量.本文作者证明在常数逆温度β下的吉布斯态(Gibbs state)有一个矩阵乘积表示,其连接维数为e^(δ(√βlog(1/c))),使得所有局部属性达到精度为∈的近似.这说明了在吉布斯态属性的数值模拟中,使用不依赖于系统大小的连接维数的常见做法是合理的.

关 键 词：矩阵乘积 吉布斯 短程相互作用 计算物理学 量子系统 多体系统 

分 类 号：O241[理学—计算数学] O413.3[理学—数学]