A bstract In this work, we explore topological phases of matter obtained by effectively gauging or fermionizing a system, where the Gauss law constraint is only enforced energetically. In contrast to conventional gauging or fermionization, the symmetry that is effectively gauged at low energies still generates a global symmetry that acts on the whole Hilbert space faithfully. This symmetry turns out to protect a nontrivial topological phase together with other symmetries, or it can carry a nontrivial emergent ’t Hooft anomaly. We provide a precise formula for the topological response action involving these symmetries in a general setup, as well as a formula for ’t Hooft anomalies. As an application, we apply the general treatment of the procedure to gapless systems and find various new gapless SPT phases, such as the one carrying the Gu-Wen fermionic anomalies at low energy.
Takamasa Ando (2026) studied this question.