About

Van der Waals heterostructures provide an outstanding platform to engineer elusive quantum phenomena, by exploiting materials engineering, twist engineering and proximity effects. These strategies allow controlling the strength of quantum many-body interactions, and tailoring the internal quantum degrees of freedom, establishing unique playground to create quantum states of matter that rely on the coexistence of antagonists electronic orders. We are interested in developing new theoretical routes to exploit the flexibility of these materials to create exotic physics not accessible in conventional compounds. On the theory side, among others, we recently showed:
- Controlling artificial gauge fields electrically in twisted graphene multilayers
- Designing frustrated valley magnets in twisted graphene multilayers
- Generating electrically controllable correlated states in twisted graphene multilayers
- Engineering artificial heavy-fermion correlated states in twisted graphene multilayers
- Revealing the mechanism leading to multiferroic order in a van der Waals monolayer
In collaboration with experimental groups, we recently experimentally demonstrated:
- Realizing an artificial many-body heavy-fermion state in van der Waals multilayers
- Probing magnetic excitations in van der Waals magnets
- Designing magnetically frustrated van der Waals magnets with spin-orbit coupling engineering
- Probing crystal field effects in twisted graphene multilayers.

The methodologies that we develop are implemented in freely available in an open source library to study electronic, interacting and topological properties of tight binding models.

Current main research lines:
- Tunable correlated quantum matter in twisted van der Waals materials
- Van der Waals multiferroics
- Heavy-fermion Kondo quantum matter in van der Waals materials

Interactions in strongly correlated materials are capable of creating exotic behaviors not existent in conventional compounds. Paradigmatic examples of this are unconventional superconducting states, strongly correlated topological states, and fractionalized particles. We are focusing on exploring new forms of quantum matter that can emerge in systems showing quasiperiodicity, strong many-body interactions, and coupling to an environment. From a methodological perspective, part of my strategy focuses on exploring these exotic states using tensor-network methods both closed systems and open quantum many-body models, and how to use this methods to simulate noisy quantum computers. Among other, we have recently shown
- Designing solitonic excitations between quantum disordered magnets and superconductors
- Designing quasiperiodic systems featuring topological excitations in purely quantum many-body systems
- Engineering topological modes in non-Hermitian interacting systems
In collaboration with experimental groups, we experimentally showed:
- Generating and probing criticality in quasiperiodic states
- Promoting topological superconducting excitations with moire patterns
- Engineering and detecting triplon excitations in a designer quantum magnet

The methods we design are also implemented in freely available open source libraries we develop to solve quantum many-body problems with tensor networks.

Current main research lines:
- Non-Hermitian interacting many-body topology
- Tensor-network methods for non-Hermitian dynamical quantum many-body matter
- Quantum-circuit tensor-network algorithms for quantum matter

A variety of problems in quantum materials remain greatly challenging with conventional methods. We are focusing on how to use generative machine learning to design quantum materials, how to solve interacting two-dimensional quantum many-body problems with neural network solvers, and how to infer Hamiltonians from experimentally available measurements with machine learning. We are focusing on developing generative machine learning algorithms provide to explore complex behavior in quantum materials, allowing the incorporation of interactions, disorder, and hidden variables. From the many-body solver perspective, neural network quantum states have risen as a greatly powerful many-body methodology for interacting systems, providing a well-suited method to solve complex correlated two-dimensional models. Finally, we are specially interested in developing strategies for Hamiltonian learning, an inverse problem of critical importance for quantum materials that cannot be solved using conventional methods in condensed matter physics. Ultimately, we aim to combine generative models and Hamiltonian learning, bringing together experimental data and theoretical models. Some of our recent demonstrations include:

-- Machine learning quantum many-body correlation entropy from local measurements
- Exploiting generative adversarial machine learning for dynamical quantum matter and Hamiltonian learning
- Predicting phase transition in quantum magnets with neural-network quantum state solvers
- Hamiltonian learning from local dynamical spectroscopy in quantum magnets
 

Current main research lines:
- Generative-adversarial machine learning for quantum materials
- Machine learning entanglement in quantum materials
- Neural-network methods for quantum criticality
- Machine learning methods for Hamiltonian learning from experimental data