Codification Volume of an operator algebra and its irreversible growth through thermal processes

Given a many-body system, we define a quantity, the Codification Volume of an operator algebra, which measures the size of the subspace with whom a given algebra is correlated. We explicitly calculate it for some limit cases, including vacuum states of local Hamiltonians and random states taken from the Haar ensemble. We argue that this volume should grow irreversibly in a thermalization process, and illustrate it numerically on a non-integrable quantum spin chain

Horn Binary Serialization Analysis

A bit layout is a sequence of fields of certain bit lengths that specifies how to interpret a serial stream, e.g., the MP3 audio format. A layout with variable length fields needs to include meta-information to help the parser interpret unambiguously the rest of the stream; e.g. a field providing the length of a following variable length field. If no such information is available, then the layout is ambiguous. I present a linear-time algorithm to determine whether a layout is ambiguous or not by modelling the behaviour of a serial parser reading the stream as forward chaining reasoning on a collection of Horn clauses.Comment: In Proceedings HCVS2016, arXiv:1607.0403

Edge insulating topological phases in a two-dimensional long-range superconductor

We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases, not continuously connected with any short-range phase, occur, signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short- range limit. The definition of a topology in the bulk and the presence of a bulk-boundary correspondence is still suggested for the long-range phases. Recent experimental proposals and advances open the stimulating possibility to probe the described long-range effects in next-future realistic set-ups