An infinite family of 3d Floquet topological paramagnets

Abstract

We uncover an infinite family of time-reversal symmetric 3d interacting topological insulators of bosons or spins, in time-periodically driven systems, which we term Floquet topological paramagnets (FTPMs). These FTPM phases exhibit intrinsically dynamical properties that could not occur in thermal equilibrium, and are governed by an infinite set of $Z_2$-valued topological invariants, one for each prime number. The topological invariants are physically characterized by surface magnetic domain walls that act as unidirectional quantum channels, transferring quantized packets of information during each driving period. We construct exactly solvable models realizing each of these phases, and discuss the anomalous dynamics of their topologically protected surface states. Unlike previous encountered examples of Floquet SPT phases, these 3d FTPMs are not captured by group cohomology methods, and cannot be obtained from equilibrium classifications simply by treating the discrete time-translation as an ordinary symmetry. The simplest such FTPM phase can feature anomalous $Z_2$ (toric code) surface topological order, in which the gauge electric and magnetic excitations are exchanged in each Floquet period, which cannot occur in a pure 2d system without breaking time reversal symmetry.

4+9 pages, 8 figures

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Cited by in corpus (12)

• Topology and Broken Symmetry in Floquet Systems
• Many-body localization, symmetry, and topology
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• Quantized large-bias current in the anomalous Floquet-Anderson insulator
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Disentangling interacting symmetry protected phases of fermions in two dimensions
• Quantum frequency locking and down-conversion in a driven cavity-qubit system
• Quantized Floquet topology with temporal noise
• Electronic Floquet Liquid Crystals
• Superuniversality from disorder at two-dimensional topological phase transitions
• Quantum cellular automata and categorical dualities of spin chains
• Symmetric entanglers for non-invertible SPT phases