Interaction Enabled Fractonic Higher-Order Topological Phases

Abstract

In this work, we present a collection of three-dimensional higher-order symmetry protected topological phases (HOSPTs) with gapless hinge modes that exist only in strongly interacting systems subject to subsystem symmetry constraints. We use a coupled wire construction to generate three families of microscopic lattice models: insulators with helical hinge modes, superconductors with chiral Majorana hinge modes, and fractionalized insulators with helical hinge modes that carry fractional charge. In particular, these HOSPTs do not require spatial symmetry protection, but are instead protected by subsystem symmetries, and support "fractonic" quasiparticle excitations that move within only a low-dimensional sub-manifold of the system. We analyze the anomaly structure for the boundary theory and the entanglement Hamiltonian, and show that the side surfaces of these HOSPTs, despite being partially gapped, exhibit symmetry anomalies, and can only be realized as the boundary of three-dimensional HOSPT phases.

Fractional second-order topological insulator from a three-dimensional coupled-wires construction

“…[7], meaning the helical hinge states are robust against local perturbations as long as both bulk and surface gaps remain open and timereversal symmetry is maintained. As opposed to previous work in a similar direction [49], where even the nonfractionalized phase required the presence of interaction terms in order to maintain the protecting subsystem symmetry, we obtain conventional hinge states with charge e from only single-particle tunnelings between nearestneighbor wires.…”

“…While the original theory of HOTIs builds on singleparticle band structure considerations, it is interesting to ask whether there are exotic interaction-driven HOTI phases that do not fit into this conventional picture. While this question has by now been answered affirmatively [45][46][47][48][49][50][51][52][53], concrete toy models for strongly interacting HOTI phases are still extremely rare since analytical tools to study interacting systems in more than one dimension are scarce. One way forward is offered by the so-called coupled-wires approach [54,55], where a twodimensional (2D) or three-dimensional (3D) system is modeled as an array of weakly coupled one-dimensional (1D) wires.…”

“…Models of coupled wires have been used with high success to study a variety of exotic interacting first-order topological phases, including, for example, fractional quantum Hall states [54,55,[57][58][59][60][61][62], fractional TIs [63][64][65][66][67][68], or interacting topological superconductors [68][69][70]. As for HOTI phases, models for strongly interacting second-order topological superconductors in two dimensions [47,48,52] and certain classes of 3D second-order TIs protected by subsystem symme-tries [49] have been brought forward. Nevertheless, a large variety of interacting HOTI phases do not yet have concrete realizations.…”

Anomalous flux state in higher-order topological superconductors

“…In the zero correlation length limit, the HOTSC model in Eq. 13 has a coupled wire construction [52]. We can decompose the complex fermions along each z-row into two up-moving and two down-moving chiral Majoranas.…”

Construction and classification of crystalline topological superconductor and insulators in three-dimensional interacting fermion systems

“…In particular, very different from SPT phases protected by internal symmetry, the boundaries of d-dimensional crystalline SPT phases are typically gapped but with protected (d − n)-dimensional gapless modes (1 < n ≤ d) at the hinges or corners. This type of topological phases are dubbed higher-order (HO) topological phases [82][83][84][85][86][87][88][89][90][91][92][93][94][95].…”