Quantum Restored Symmetry Protected Topological Phases

Abstract: Symmetry protected topological (SPT) phases are fundamental quantum many-body states of matter beyond Landau's paradigm. Here, we introduce the concept of quantum restored SPTs (QRSPTs), where the protecting symmetry is spontaneously broken at each instance in time, but restored after time average over quantum fluctuations, so that topological features re-emerge. To illustrate the concept, we study a one-dimensional fermionic Su-Schrieffer-Heeger model with fluctuating superconducting order. We solve this problem in several limiting cases using a variety of analytical methods and compare them to numerical (density matrix renormalization group) simulations which are valid throughout the parameter regime. We thereby map out the phase diagram and identify a QRSPT phase with topological features which are reminiscent from (but not identical to) the topology of the underlying free fermion system. The QRSPT paradigm thereby stimulates a new perspective for the constructive design of novel topological quantum many-body phases.