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Higher-order topological quantum paramagnets

Quantum paramagnets are strongly-correlated phases of matter where competing interactions frustrate magnetic order down to zero temperature. In certain cases, quantum fluctuations induce instead topological order, supporting, in particular, fractionalized quasi-particle excitations. In this work, we investigate paradigmatic spin models and show how magnetic frustration can also give rise to higher-order topological properties. We first study the frustrated Heisenberg model in a square lattice, where a plaquette valence bond solid appears through the spontaneous breaking of translational invariance. Despite the amount of effort that has been devoted to study this phase, its topological nature has so far been overlooked. By means of tensor network simulations, we establish how such state belongs to a higher-order symmetry-protected topological phase, where long-range plaquette order and non-trivial topology coexist. This interplay allows the system to support excitations that would be absent otherwise, such as corner-like states in the bulk attached to dynamical topological defects. Finally, we demonstrate how this higher-order topological quantum paramagnet can also be induced by dipolar interactions, indicating the possibility to directly observe this phase using atomic quantum simulators.