论文标题
高斯矩阵产品状态无法有效地描述关键系统
Gaussian matrix product states cannot efficiently describe critical systems
论文作者
论文摘要
高斯费米子基质量态（GFMPS）形成了一类ANSATZ量子状态，用于非互动费米子的1D系统。我们显示，对于一个简单的自由跳跃费米子的关键模型，：（i）任何GFMPS与基态的任何GFMP近似都必须具有键尺寸的键尺度，以系统尺寸进行超单层缩放，而（ii）则存在非高斯费米子MPS近似与该状态的多项键键尺寸。这证明，通常，在张量网络的水平上强加高斯可能会显着改变其有效近似关键高斯州的能力。我们还提供了数值证据，表明所需的债券维度是次指数的，因此仍然可以使用中等资源进行模拟。
Gaussian fermionic matrix product states (GfMPS) form a class of ansatz quantum states for 1d systems of noninteracting fermions. We show, for a simple critical model of free hopping fermions, that: (i) any GfMPS approximation to its ground state must have bond dimension scaling superpolynomially with the system size, whereas (ii) there exists a non-Gaussian fermionic MPS approximation to this state with polynomial bond dimension. This proves that, in general, imposing Gaussianity at the level of the tensor network may significantly alter its capability to efficiently approximate critical Gaussian states. We also provide numerical evidence that the required bond dimension is subexponential, and thus can still be simulated with moderate resources.
