Multikink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF field theories

Abstract

Quantum disordering a discrete-symmetry-breaking state by condensing domain walls can lead to a trivial symmetric insulator state. In this work, we show that if we bind a one-dimensional representation of the symmetry (such as a charge) to the intersection point of several domain walls, condensing such modified domain walls can lead to a nontrivial symmetry-protected topological (SPT) state. This result is obtained by showing that the modified domain-wall condensed state has a nontrivial SPT invariant, the symmetry-twist-dependent partition function. We propose two different kinds of field theories that can describe the above-mentioned SPT states. The first one is a Ginzburg-Landau–type nonlinear sigma model theory, but with an additional multikink domain-wall topological term. Such theory has an anomalous U[superscript k](1) symmetry but an anomaly-free Z[k over N] symmetry. The second one is a gauge theory, which is beyond Abelian Chern-Simons/BF gauge theories. We argue that the two field theories are equivalent at low energies. After coupling to the symmetry twists, both theories produce the desired SPT invariant.