标题： 通过规范不变的VUMPS研究施温格模型的临界行为 显示英文标题

标题： Critical behavior of the Schwinger model via gauge-invariant VUMPS

摘要： 我们通过将变分均匀矩阵乘积态（VUMPS）算法与局部施加高斯定律约束的规范不变矩阵乘积假设相结合，研究了格点施温格模型。 连续体和格点版本的施温格模型，当$\theta=\pi$时，已知在费米子质量高于临界值的范围内表现出一阶相变，其中第二阶相变发生。 我们的算法使我们能够精确确定连续体理论中的临界端点。 我们进一步分析了同时处于临界和连续极限下的标度，并确认数据坍缩与伊辛普适类非常精确地一致。 显示英文摘要

摘要： We study the lattice Schwinger model by combining the variational uniform matrix product state (VUMPS) algorithm with a gauge-invariant matrix product ansatz that locally enforces the Gauss law constraint. Both the continuum and lattice versions of the Schwinger model with $\theta=\pi$ are known to exhibit first-order phase transitions for the values of the fermion mass above a critical value, where a second-order phase transition occurs. Our algorithm enables a precise determination of the critical endpoint in the continuum theory. We further analyze the scaling in the simultaneous critical and continuum limits and confirm that the data collapse aligns with the Ising universality class to remarkable precision.