无截止量子场的相对论连续矩阵乘积态
Relativistic continuous matrix product states for quantum fields without cutoff
摘要：
我介绍了一个修改的连续矩阵乘积态（CMPS），使他们适应相对论量子场论（QFT）。这些相对论CMPS可以用来解决真正的1 + 1维QFT没有UV截止和直接在热力学极限。其主要思想是直接在对角化所考虑的模型的自由部分的基础上工作，这允许精确地拟合其短距离行为。这使得计算比标准CMPS稍微不那么琐碎。然而，它们仍然是可行的，我提出了优化所需的所有步骤。渐近成本作为键尺寸的函数保持与标准CMPS相同。我说明了自相互作用的标量场的方法，又名。$ϕ^4_2$模型。除了提供无与伦比的精度在连续，得到的数值结果是真正的变分，从而提供严格的能量上限。
英文摘要：
I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV cutoff and directly in the thermodynamic limit. The main idea is to work directly in the basis that diagonalizes the free part of the model considered, which allows to fit its short distance behavior exactly. This makes computations slightly less trivial than with standard CMPS. However, they remain feasible and I present all the steps needed for the optimization. The asymptotic cost as a function of the bond dimension remains the same as for standard CMPS. I illustrate the method on the self-interacting scalar field, a.k.a. the $ϕ^4_2$ model. Aside from providing unequaled precision in the continuum, the numerical results obtained are truly variational, and thus provide rigorous energy upper bounds.
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