标题： 相互作用格点费米子在正温度下的磁化强度与边缘电流相等 显示英文标题

标题： Equality of magnetization and edge current for interacting lattice fermions at positive temperature

摘要： 我们证明，在满足局部不可区分性的吉布斯态的有限范围相互作用格点费米子模型的大类中，磁化强度在热力学极限下等于边缘电流，这一条件在足够高温下已知成立。 我们的结果表明，此类系统中的边缘电流由体性质决定，因此在边界附近的大扰动下是稳定的。 此外，在对化学势求导后，这种等式仍然成立。 我们表明，这种体-边对应形式基本上是由于体的均匀性和吉布斯态的局部性。 一个重要的中间结果是二维系统的布洛赫定理的新版本，该定理指出持久电流在体中消失。 显示英文摘要

摘要： We prove that the magnetization is equal to the edge current in the thermodynamic limit for a large class of models of lattice fermions with finite-range interactions satisfying local indistinguishability of the Gibbs state, a condition known to hold for sufficiently high temperatures. Our result implies that edge currents in such systems are determined by bulk properties and are therefore stable against large perturbations near the boundaries. Moreover, the equality persists also after taking the derivative with respect to the chemical potential. We show that this form of bulk-edge correspondence is essentially a consequence of homogeneity in the bulk and locality of the Gibbs state. An important intermediate result is a new version of Bloch's theorem for two-dimensional systems, stating that persistent currents vanish in the bulk.