**Principal Investigator (PI):** dr.sc. Fabio Franchini - Research Associate, RBI

**Collaborators:**- dr.sc. Ivan Balog - Research Associate, Institute of Physics
- dr.sc. Vinko Zlatić - Research Associate, RBI

**Foreseen future collaborators (approved appointments):**- one PhD student
- one postdoc student

**Starting date:** 1st of May, 2017

**Ending date:** 30th of April, 2021

More is Different wrote P.W. Anderson in 1972, explaining that the central challenge of modern physics is to understand how the interaction of a large number of elementary constituents can lead to the emergence of novel, complex behaviors, which can hardly be explained in terms of the original ingredients.

In order to identify the appropriate variables and formalism to capture the behavior of a few prototypical toy models, we will assemble expertise in different types of complex systems.

On one side, we will use a toy model understand the relation between a novel spontaneous symmetry breaking (SSB), localization and glassiness, with applications in condensed matter and complex systems. This model is formulated in terms of large matrices and has already been linked to the metal/insulator transition from one side, and to the Chern-Simons/topological string theories from another. More recently, it was understood that the conjectured nontrivial SSB realized in this model is the reflection of a complex energy landscape, characterized by a parametrically large number of equilibrium. Such a behavior is paradigmatic of a complex system and thus it can be captured by a new type of replica symmetry breaking.

In a parallel effort, we will use a one dimensional model with long range interaction as a tool to model the behavior of the random field Ising model in different dimensions and to study the critical exponents and avalanche phenomenology. In the toy model, the effective dimension is encoded in decay rate of the long range interaction and thus allow for a fine tuning even to relevant “fractional” dimensions emerging from non-perturbative-RG.

We will also tackle strongly interacting quantum systems and their entanglement properties, to understand how information theory can help in discriminating the special nature of multi-critical, non-conformal points and the computational power of topological phases through non-local convertibility.

dr.sc. Fabio Franchini, principal investigator

Condensed Matter and Statistical Physics Group

Division of Theoretical Physics

Rudjer Boskovic Institute

Zagreb, Croatia

E-mail: Fabio.Franchini@irb.hr

tel: +385-1-4560214