**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
- dr.sc. Vinko Zlatić - Senior Research Associate, RBI
- dr.sc. Andrey Federenko - Research Associate, ENS de Lyon
- dr.sc. Domagoj Kuić - Postdoctoral researcher, RBI
- Vanja Marić - PhD student, SISSA/RBI
- Luka Sinković - PhD student, PMF/Institute of Physics

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

**Ending date:** 31th of August, 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.

- "Modern Aspects of Quantum Physics", October 1st — 5th, 2018; Ruđer Bošković Institute, Zagreb, Croatia, Organizers: Fabio Franchini & Ugo Marzolino

- F. Benatti, R. Floreanini, F. Franchini, U. Marzolino, "Remarks on entanglement and identical particles", Open Systems & Information Dynamics Vol. 24, no. 03, 1740004 (2017)
- Ivan Balog, David Carpentier , and Andrei A. Fedorenko: ``Disorder-driven quantum transition in relativistic semimetals: functional renormalization via the porous medium equation", Phys. Rev. Lett. 121, 166402 (2018)
- Salvatore Marco Giampaolo, Flávia Braga Ramos, and Fabio Franchini, "The Frustration in being Odd: Universal area law violation in local systems" J. Phys. Commun. 3 081001 (2019), 10
- Ivan Balog, Gilles Tarjus, Matthieu Tissier, ´´Comment on "Evidence for Supersymmetry in the Random-Field Ising Model at D=5''", arXiv:1906.10058 (2019)
- V. Marić, S.M. Giampaolo, D. Kuić, F. Franchini, "The Frustration of being Odd: How Boundary Conditions can destroy Local Order", arXiv:1908.10876
- V. Marić, S. M. Giampaolo, & F. Franchini, “The Frustration of being Odd: Can Boundary Conditions induce a Quantum Phase Transition?", arXiv:2002.07197
- V. Marić & F. Franchini; ""Asymptotic behavior of Toeplitz determinants with delta function singularities", arXiv:2006.01922
- V. Marić, F. Franchini, D. Kuić, & S. M. Giampaolo, "The Frustration of being Odd: Resilience of the Topological Phases", arXiv:2006.09397

- Fabio Franchini: "The Frustration in Being Odd: Area Law Violation in Local Systems", "INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS", ICTS- TIFR, Bangalore, Indija, 30.07.2018 - 10.08.2018
- Fabio Franchini: "Introduction to Bethe Ansatz", "INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS", ICTS- TIFR, Bangalore, Indija, 30.07.2018 - 10.08.2018 -Fabio Franchini: "The Frustration in Being Odd: Area Law Violation in Local Systems", "Conference on Physics of Defects in Solids: Quantum Mechanics Meets Topology | (smr 3221)", ICTP, Trieste, Italija, 09.07.2018 - 13.07.2018
- Fabio Franchini: "A primer on Integrable Techniques", Institut Rudjer Boskovic, Zagreb (Hrvatska), 06.03.2018 - 06.05.2018
- Ivan Balog: "Hysteresis transition in the Random field Ising model", "11th Symposium on Hysteresis Modeling and Micromagnetics", University of Barcelona, Španjolska, 29.05.2017 - 31.05.2017
- Ivan Balog: "Metal-semimetal transition in Weyl fermions as a self-focusing phenomenon in non-linear diffusion" "Conference on Weyl Fermions in Materials | (smr 3157)", ICTP, Trieste, Italija, 23.10.2017 - 27.10.2017
- Fabio Franchini: "The Frustration of being Odd: Universal Area Law violation in local systems", Univerza v Ljubljani, 18.09.2018
- Fabio Franchini: "The Frustration of being Odd: Universal Area Law violation in local systems", IRB, Zagreb, 12.10.2018
- Fabio Franchini: "The Frustration of being Odd: Universal Area Law violation in local systems", Simons Center For Geometry and Physics, Stony Brook (NY,USA), 18.10.2018
- Fabio Franchini: "The Frustration of being Odd: Universal Area Law violation in local systems", University of Massachusetts Boston (MA, USA), 23.10.2018
- Fabio Franchini: "The Frustration of being Odd: Universal Area Law violation in local systems", SISSA, Trieste (ITALY), 06.11.2018
- Fabio Franchini: "Spontaneous Ergodicity Breaking in Invariant Matrix Models", LPTMS, Orsay, Paris (France), 15.01.2019
- Fabio Franchini" "The Frustration of being Odd: Universal Area Law violation in local systems", "Breakdown Of Ergodicity In Isolated Quantum Systems: From Glassiness To Localization", Arcetri's Galileo Galilei Institute, Florence (Italy), 20.05.2019 - 12.07.2019
- Fabio Franchini: "The Frustration of being Odd: Universal Area Law violation in local systems", King's College, London (UK), 26.06.2019
- Vanja Marić: "Magnetization in the Frustrated XY chain", ECAMP13, Florence (Italy), 08.04.2019 - 12.04.2019 (Poster)
- Domagoj Kuić: "Frustration in the cluster-Ising ring with odd number of spins", ECAMP13, Florence (Italy), 08.04.2019 - 12.04.2019 (Poster)
- Ivan Balog: "Metal-semimetal transition in Weyl fermions as a self-focusing phenomenon in non-linear diffusion", "Novel Aspects of Quantum Physics",IRB, Zagreb (Hrvatska) 01.10.2018 - 05.10.2018
- Ivan Balog: "Metal-semimetal transition in Weyl fermions as a self-focusing phenomenon in non-linear diffusion", Zagreb, PMF (Hrvatska) 02.11.2018 - 03.11.2018
- Qualifying Exam presentation at SISSA, Trieste, April 2019.
- Presentation at Humboldt Kolleg Conference, Zagreb, October 2019.
- Student's presentation at RBI, Zagreb, October 2019.
- Poster at the conference EGAS 51 / ECAMP 13, Florence, April 2019.

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