标题： 薛丁格模型的临界行为通过规范不变的VUMPS研究 显示英文标题

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

摘要： 我们通过结合变分均匀矩阵乘积态（VUMPS）算法与一种规范不变的矩阵乘积假设来研究晶格施温格模型，该假设局部强制高斯定律约束。 已知当费米子质量超过临界值时，具有$\theta=\pi$的连续统和晶格版本的施温格模型会出现一阶相变，在此临界值处会发生二阶相变。 我们的算法能够精确确定连续统理论中的临界端点。 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惊人地一致。 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.