Entanglement Entropy in 2D Non-abelian Pure Gauge Theory

We compute the Entanglement Entropy (EE) of a bipartition in 2D pure non-abelian $U(N)$ gauge theory. We obtain a general expression for EE on an arbitrary Riemann surface. We find that due to area-preserving diffeomorphism symmetry EE does not depend on the size of the subsystem, but only on the number of disjoint intervals defining the bipartition. In the strong coupling limit on a torus we find that the scaling of the EE at small temperature is given by $S(T) - S(0) = O\left(\frac{m_{gap}}{T}e^{-\frac{m_{gap}}{T}}\right)$, which is similar to the scaling for the matter fields recently derived in literature. In the large $N$ limit we compute all of the Renyi entropies and identify the Douglas-Kazakov phase transition.Comment: 6 page

Divide and conquer: resonance induced by competitive interactions

We study an Ising model in a network with disorder induced by the presence of both attractive and repulsive links. This system is subjected to a subthreshold signal, and the goal is to see how the response is enhanced for a given fraction of repulsive links. This can model a network of spin-like neurons with excitatory and inhibitory couplings. By means of numerical simulations and analytical calculations we find that there is an optimal probability, such that the coherent response is maximal

Bulk-Edge correspondence of entanglement spectrum in 2D spin ground states

General local spin $S$ ground states, described by a Valence Bond Solid (VBS) on a two dimensional lattice are studied. The norm of these ground states is mapped to a classical O(3) model on the same lattice. Using this quantum-to-classical mapping we obtain the partial density matrix $\rho_{A}$ associated with a subsystem ${A}$ of the original ground state. We show that the entanglement spectrum of $\rho_{\rm A}$ in a translation invariant lattice is given by the spectrum of a quantum spin chain at the boundary of region $A$, with local Heisenberg type interactions between spin 1/2 particles.Comment: 8 pages, 4 figures, one section and references adde