



01306nas a2200121   4500008004100000245007000041210006900111260001500180520091800195100001601113700001801129856003701147       2021                        eng d00aExactly Solvable Lattice Hamiltonians and Gravitational Anomalies0 aExactly Solvable Lattice Hamiltonians and Gravitational Anomalie  c10/27/20213 a<p>We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary Z2 topological order with fermionic particle and fermionic loop excitations that have mutual π statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary Z2 symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.</p>1 aChen, Yu-An1 aHsin, Po-Shen  uhttps://arxiv.org/abs/2110.14644