Local response of topological order to an external perturbation

We study the behavior of the R\'enyi entropies for the toric code subject to a variety of different perturbations, by means of 2D density matrix renormalization group and analytical methods. We find that R\'enyi entropies of different index {\alpha} display derivatives with opposite sign, as opposed to typical symmetry breaking states, and can be detected on a very small subsystem regardless of the correlation length. This phenomenon is due to the presence in the phase of a point with flat entanglement spectrum, zero correlation length, and area law for the entanglement entropy. We argue that this kind of splitting is common to all the phases with a certain group theoretic structure, including quantum double models, cluster states, and other quantum spin liquids. The fact that the size of the subsystem does not need to scale with the correlation length makes it possible for this effect to be accessed experimentally.Comment: updated to published versio

Geological survey of Maryland using EREP flight data

The author has identified the following significant results. Underflight photography has been used in the Baltimore County mined land inventory to determine areas of disturbed land where surface mining of sand and ground clay, or stone has taken place. Both active and abandoned pits and quarries were located. Aircraft data has been used to update cultural features of Calvert, Caroline, St. Mary's, Somerset, Talbot, and Wicomico Counties. Islands have been located and catalogued for comparison with older film and map data for erosion data. Strip mined areas are being mapped to obtain total area disturbed to aid in future mining and reclamation problems. Coastal estuarine and Atlantic Coast features are being studied to determine nearshore bedforms, sedimentary, and erosional patterns, and manmade influence on natural systems

Lieb-Robinson bounds for commutator-bounded operators

We generalize the Lieb-Robinson theorem to systems whose Hamiltonian is the sum of local operators whose commutators are bounded.Comment: 5 pages, minor editorial change

Magnonic triply-degenerate nodal points

We generalize the concept of triply-degenerate nodal points to non-collinear antiferromagnets. Here, we introduce this concept to insulating quantum antiferromagnets on the decorated honeycomb lattice, with spin-$1$ bosonic quasiparticle excitations known as magnons. We demonstrate the existence of magnonic surface states with constant energy contours that form pairs of magnonic arcs connecting the surface projection of the magnonic triple nodal points. The quasiparticle excitations near the triple nodal points represent three-component bosons beyond that of magnonic Dirac, Weyl, and nodal-line cases. They can be regarded as a direct reflection of the intrinsic spin carried by magnons. Furthermore, we show that the magnonic triple nodal points can split into magnonic Weyl points, as the system transits from a non-collinear spin structure to a noncoplanar one with a nonzero scalar spin chirality. Our results not only apply to insulating antiferromagnets, but also provide a platform to seek for triple nodal points in metallic antiferromagnets.Comment: 6 pages, 5 figures + Supplemental Material. To appear in EPL (Europhys. Lett.