Entanglement of quantum spin systems: a valence-bond approach

In order to quantify entanglement between two parts of a quantum system, one of the most used estimator is the Von Neumann entropy. Unfortunately, computing this quantity for large interacting quantum spin systems remains an open issue. Faced with this difficulty, other estimators have been proposed to measure entanglement efficiently, mostly by using simulations in the valence-bond basis. We review the different proposals and try to clarify the connections between their geometric definitions and proper observables. We illustrate this analysis with new results of entanglement properties of spin 1 chains.Comment: Proceedings of StatPhys 24 satellite conference in Hanoi; submitted for a special issue of Modern Physics Letters

Valence bond entanglement entropy of frustrated spin chains

We extend the definition of the recently introduced valence bond entanglement entropy to arbitrary SU(2) wave functions of S=1/2 spin systems. Thanks to a reformulation of this entanglement measure in terms of a projection, we are able to compute it with various numerical techniques for frustrated spin models. We provide extensive numerical data for the one-dimensional J1-J2 spin chain where we are able to locate the quantum phase transition by using the scaling of this entropy with the block size. We also systematically compare with the scaling of the von Neumann entanglement entropy. We finally underline that the valence-bond entropy definition does depend on the choice of bipartition so that, for frustrated models, a "good" bipartition should be chosen, for instance according to the Marshall sign.Comment: 10 pages, 6 figures; v2: published versio

Melonic phase transition in group field theory

Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for the melonic amplitudes in terms of a graph polynomial related to a higher dimensional generalization of the Kirchhoff tree-matrix theorem. Simple bounds on these amplitudes show the existence of a phase transition driven by melonic interaction processes. We restrict our study to the Boulatov-Ooguri models, which describe topological BF theories and are the basis for the construction of four dimensional models of quantum gravity.Comment: 8 pages, 4 figures; to appear in Letters in Mathematical Physic

Measurement of the linear thermo-optical coefficient of Ga0.51_{0.51}In0.49_{0.49}P using photonic crystal nanocavities

Ga$_{0.51}$In$_{0.49}$P is a promising candidate for thermally tunable nanophotonic devices due to its low thermal conductivity. In this work we study its thermo-optical response. We obtain the linear thermo-optical coefficient $dn/dT=2.0\pm0.3\cdot 10^{-4}\,\rm{K}^{-1}$ by investigating the transmission properties of a single mode-gap photonic crystal nanocavity.Comment: 7 pages, 4 figure

Tuning out disorder-induced localization in nanophotonic cavity arrays

Weakly coupled high-Q nanophotonic cavities are building blocks of slow-light waveguides and other nanophotonic devices. Their functionality critically depends on tuning as resonance frequencies should stay within the bandwidth of the device. Unavoidable disorder leads to random frequency shifts which cause localization of the light in single cavities. We present a new method to finely tune individual resonances of light in a system of coupled nanocavities. We use holographic laser-induced heating and address thermal crosstalk between nanocavities using a response matrix approach. As a main result we observe a simultaneous anticrossing of 3 nanophotonic resonances, which were initially split by disorder.Comment: 11 page