论文标题
多项式相互作用的基质产品操作员表示
Matrix product operator representation of polynomial interactions
论文作者
论文摘要
我们在一维晶格上提供了相互作用的相互作用的构造，该晶格的多项式生长，将指数乘以晶格位点分离为基质产品操作员（MPO），矩阵产品操作员（MPO）是一种一维张量网络。我们表明，对于订单$ k $的多项式，债券尺寸为$（k+3）$，独立于系统大小和粒子数。我们的构造显然是翻译不变的，因此可以用于有限或无限大小的变异矩阵产品状态算法中。我们的结果为多体量子运算符的相关结构提供了新的见解，并且在对多体系统的模拟中也可能是实用的，这些系统的相互作用在大距离上呈指数筛选，但可能具有复杂的短距离结构。
We provide an exact construction of interaction Hamiltonians on a one-dimensional lattice which grow as a polynomial multiplied by an exponential with the lattice site separation as a matrix product operator (MPO), a type of one-dimensional tensor network. We show that the bond dimension is $(k+3)$ for a polynomial of order $k$, independent of the system size and the number of particles. Our construction is manifestly translationally invariant, and so may be used in finite- or infinite-size variational matrix product state algorithms. Our results provide new insight into the correlation structure of many-body quantum operators, and may also be practical in simulations of many-body systems whose interactions are exponentially screened at large distances, but may have complex short-distance structure.
