## Research

My interest lies in the condensed matter physics field. I am a theorist who enjoys designing simple experiments when the occasion permits. My work focuses on magnetism and elasticity theories: I consider the study of materials with competing interactions a reliable and elegant attempt to find and understand novel states of matter. All the more, the comprehension of such materials may prove useful in technological applications such as computer memory based on magnetic circuits and computers that rely on quantum operations.

Below I give a summary of some of my past and ongoing work.

Projective symmetry of partons in Kitaev's honeycomb model:

Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We have recently studied the spectrum of Majorana fermions of Kitaev's honeycomb model on spherical clusters ref.11 (and second figure from left to right at Home). The gauge field endows the partons with half-integer orbital angular momenta. We found that the structure of parton multiplets can be understood in the framework of projective symmetries, which combine physical and gauge transformations. For all spherical clusters we examined, the projective symmetry group for the ground state is the double cover of the point group. As far as we know, this is the first application of projective symmetries in a solvable model of a spin liquid.

Topological Defects in the Kitaev Model:

Quantum computing in which operations are robust against noise, could endow us with tools that boost our current ability to solve a variety of problems far beyond physics. It is an ongoing challenge to produce and understand model systems that realize this goal. I am currently working in the understanding of topological defects in the Kitaev model, as an attempt to tackle this problem. In ref.8 we studied the gapped phase of Kitaev's honeycomb model in the presence of lattice defects. We found that some dislocations and bond defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a Z_2 gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z_2 vortex around a dislocation. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes.

Frustrated Magnetism:

The understanding of the magnetization dynamics of artificial spin ices was a main topic during my graduate studies. Using a coarse grained description, we formulated a discrete model in the kagome lattice, where magnetization dynamics is mediated by domain walls carrying magnetic charge. Interactions between magnetic charges (leftmost fig. at Home and ref. 2) compete with the effects of quenched disorder in these systems. Our results led us to understand the magnetization dynamics in real mesoscopic samples, for the case of low disorder. In these samples, positive feedback from charge redistribution is responsible for magnetic avalanches observed in experimental situations in the honeycomb lattice. Next, we studied the dipolar spin ice model in the kagome lattice at the micro-scale. The presence of residual magnetic charges in honeycomb ice, even at low temperatures, results in a sequence of two-phase transitions as its temperature is lowered. (ref. 4)

Two years later, during my postdoc, we created the first realization of magnetic frustration at the macro-scale in the honeycomb lattice, to find once again, new physics. Indeed the array of 2 cm length ferromagnetic rotors arranged in a kagome lattice, dynamically evolves into a spin-ice phase after a magnetic quench: a polarized initial state of this system settles into the honeycomb spin ice phase, with relaxation on multiple time scales. The relaxation process can be understood in terms of Coulombic interactions between magnetic charges located at the ends of the magnets and viscous dissipation at the hinges (third and fourth figures from left to right at Home and ref. 7). Our study showed how macroscopic frustration arises in a purely classical setting that is amenable to experiment, easy manipulation, theory, and computation.

Currently, I am interested in understanding the static and dynamics of frustrated artificial spin ice systems at the macro scale. Part of my work focuses on studying the resonances, dynamics, and wave phenomena in lattices of magnetic altitudinal rotors, with and without magnetic defects or vacancies.

Elasticity:

Every day life may be an effective source of inspiration for designing simple experiments. If we are not extremely lucky, phenomena happening in front of us can be translated into the elasticity theory language, and lead to novel results. As a graduate student, I worked on the implementation and solution of two problems inspired by this manner. In one of them, by studying the stretching of geometrically constrained self- avoiding membranes (rightmost fig. at Home and ref. 3), we realized a mechanism for enhancing the energy dissipation in structures under extreme deformations. On the other, our work on the wrinkling patterns generated in a bilayer membrane (realized by a painted balloon) is lending insight into the buckling of biological membranes during growth (ref. 1).

Grants

"Of two Spin Liquids: a classical and a quantum frustrated magnet". Fondecyt, Grant No 1160239. 2016 - 2019.

"Thermodynamics of two dimensional Spin Ice". Fondecyt, Grant No 11121397. 2012 - 2015.

"Geometry and applications of interacting elastic bodies". Conicyt. PAI, Grant No 79112004. 2012 - 2015.

"Magnetoelectric effect in magnetic dipolar systems". Fondecyt No 1210083. 2021-2025