标题： 临界矩阵乘积态中的自同构点：有限纠缠尺度的有效场理论 显示英文标题

标题： Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling

摘要： 我们为具有有限键维数的矩阵乘积态(MPS)的重整化流建立了一个有效场论公式，重点研究接近共形不变临界固定点的系统表现出的有限纠缠标度。 我们表明，有限MPS键维数$\chi$等价于对固定点哈密顿量引入一个相关算符的扰动。 这种机制的特征编码在与$\chi$无关的通用转移矩阵的间隙比中，这些间隙比不同于未受扰的共形场论所预测的值。 这一现象定义了一个重整化群自相似点，在该点上，由于两种效应的平衡，相关耦合常数停止流动；当增加$\chi$时，由关联长度$\xi(\chi)$设定的红外尺度增大，而晶格尺度上的扰动强度则减小。 自相似点的存在不会改变有限纠缠标度假设的有效性，因为自相似点位于临界固定点的有限距离处，处于共形场论的标度区域内。 我们通过伊辛模型的精确解和有效晶格模型的密度矩阵重整化群(DMRG)模拟的数值证据来验证这一框架。 显示英文摘要

摘要： We set up an effective field theory formulation for the renormalization flow of matrix product states (MPS) with finite bond dimension, focusing on systems exhibiting finite-entanglement scaling close to a conformally invariant critical fixed point. We show that the finite MPS bond dimension $\chi$ is equivalent to introducing a perturbation by a relevant operator to the fixed-point Hamiltonian. The fingerprint of this mechanism is encoded in the $\chi$-independent universal transfer matrix's gap ratios, which are distinct from those predicted by the unperturbed Conformal Field Theory. This phenomenon defines a renormalization group self-congruent point, where the relevant coupling constant ceases to flow due to a balance of two effects; When increasing $\chi$, the infrared scale, set by the correlation length $\xi(\chi)$, increases, while the strength of the perturbation at the lattice scale decreases. The presence of a self-congruent point does not alter the validity of the finite-entanglement scaling hypothesis, since the self-congruent point is located at a finite distance from the critical fixed point, well inside the scaling regime of the CFT. We corroborate this framework with numerical evidences from the exact solution of the Ising model and density matrix renormalization group (DMRG) simulations of an effective lattice model.