Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su(1|1) supersymmetric spin chains with long-range interactions which includes as particular cases the su(1|1) Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su(1|1) permutation operator and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low-energy excitations and the low-temperature behavior of the free energy, which coincides with that of a (1+1)-dimensional conformal field theory (CFT) with central charge c=1 when the chemical potential lies in the critical interval (0,E(π)), E(p) being the dispersion relation. We also analyze the von Neumann and Rényi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson (1+1)-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge c=1. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su(1|1) elliptic chain.

Toy model to describe the effect of positional blocklike disorder in metamaterials composites

We study theoretically the effect of a new type of blocklike positional disorder on the effective electromagnetic properties of one-dimensional chains of resonant, high-permittivity dielectric particles, where particles are arranged into perfectly well-ordered blocks whose relative position is a random variable. This creates a finite order correlation length that mimics the situation encountered in metamaterials fabricated through self-assembled techniques, whose structures often display short-range order between near neighbors but long-range disorder, due to stacking defects. Using a spectral theory approach combined with a principal component statistical analysis, we study, in the long-wavelength regime, the evolution of the electromagnetic response when the composite filling fraction and the block size are changed. Modifications in key features of the resonant response (amplitude, width, etc.) are investigated, showing a regime transition for a filling fraction around 50%.

Synchronization of Heteroclinic Circuits Through Learning in Chains of Neural Motifs

The synchronization of oscillatory activity in networks of neural networks is usually implemented through coupling the state variables describing neuronal dynamics. In this study we discuss another but complementary mechanism based on a learning process with memory. A driver network motif, acting as a teacher, exhibits winner-less competition (WLC) dynamics, while a driven motif, a learner, tunes its internal couplings according to the oscillations observed in the teacher. We show that under appropriate training the learner motif can dynamically copy the coupling pattern of the teacher and thus synchronize oscillations with the teacher. Then, we demonstrate that the replication of the WLC dynamics occurs for intermediate memory lengths only. In a unidirectional chain of N motifs coupled through teacher-learner paradigm the time interval required for pattern replication grows linearly with the chain size, hence the learning process does not blow up and at the end we observe phase synchronized oscillations along the chain. We also show that in a learning chain closed into a ring the network motifs come to a consensus, i.e. to a state with the same connectivity pattern corresponding to the mean initial pattern averaged over all network motifs.