Junior Professor of Physics at IHES

I am a theoretical physicist investigating the interplay between the notions of topology, generalised symmetry and duality, from condensed matter to high-energy physics. Welcome to my personal webpage!
In essence, my current research deals with two questions: What are the algebraic structures underlying the low-energy physics of quantum lattice many-body systems? How can the knowledge of these algebraic structures be harnessed in order to systematically unveil concealed properties, develop classifying schemes, construct innovative physical models, and, in a broader context, understand the space of quantum lattice models?
In recent years, part of my research has boiled down to translating "abstract nonsensical" constructions pertaining to (higher) category theory into tangible physical objects. Tensor networks have emerged as a crucial tool in shaping such a dictionary. Very versatile, I have also used tensor networks in the past to compute real-space renormalisation group flows a research direction I intend to revisit in the near future.


08/04/2024 Lectures
As part of the Topological order: Anyons and Fractons school in Les Houches, I will be giving a series of lectures on "Topological order in (3+1)d".
19/03/2024 Conference talk
While attending the Higher categorical tools for quantum phases of matter workshop at the Perimeter Institute, I gave a talk on "Topological sectors in quantum lattice models".
06/03/2024 Publication
Our second article with L. Lootens and F. Verstraete on dualities in one-dimensional quantum lattice models was published in PRXQ.
26/02/2024 Seminar
I am giving a Mathematical Physics seminar at CEA/IPhT on "Symmetry and duality in anyonic chains".
13/02/2024 Seminar
While visiting the University of Amsterdam, I will give a talk on "Symmetry topological field theory and non-abelian Kramers-Wannier duality of generalised Ising models".
29/11/2023 Seminar
I am giving a talk on "Dualities in quantum lattice models" at the Coll├Ęge de France
12/10/2023 Postdoc openings
We are currently hiring postdocs in theoretical physics to join the IHES!
12/10/2023 Seminar
I am giving a blackboard seminar on "Dualities in (1+1)d quantum lattice models" at the LPTMC.
01/10/2023 New position
Starting October 1st, I am joining the Institut des Hautes Etudes Scientifiques (IHES) as Junior Professor of Physics.
29/06/2023 Publication
Our first article with L. Lootens, G. Ortiz and F. Verstraete on dualities in one-dimensional quantum lattice models was published in PRXQ.
16/05/2023 Seminar
I gave an online Symmetry Seminar on "Higher categorical symmetries and gauging on the lattice".
25/04/2023 Seminar
While visiting Queen Mary University, I gave a seminar on "Generalised symmetries and dualities on the lattice".
15/03/2023 Seminar
I gave a theory seminar at Washington University St. Louis on "Higher catgorical symmetries and gauging in two-dimensional spin models".

Research highlights

Kandinsky, Composition VIII, 1923

Higher categorical symmetries and gauging in two-dimensional spin models

Higher categorical symmetries have received widespread attention in recent years. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. In this manuscript, we introduce a framework that addresses two questions: Given a two-dimensional spin model, how to gauge any of its sub-symmetries? What are the lattice symmetry operators of the resulting model? Our framework relies on an approach to dualities whereby dual lattice models only differ in a choice of module 2-category over some input fusion 2-category.
Wright, The alchemist discovering phosphorus, 1771

Dualities in one-dimensional quantum lattice models

Guided by a modern viewpoint on symmetry in terms of topological operators, we developed in these two manuscripts a systematic approach to dualities in (1+1)d quantum lattice models. Given an arbitrary model, we explain how to decompose it into superselection sectors and explicitly construct all its duals. Furthermore, we provide the lattice operators performing the transmutation of dual Hamiltonians onto one another as well as the mapping of superselection sectors, which in turns allows to address the long-standing problem of relating the spectra of dual models.
Magritte, La D├ęcalcomanie, 1966

Tensor network approach to electromagnetic duality in (3+1)d topological gauge models

This manuscript outlines a tensor network approach to (3+1)d topological phases of matter. Given a (3+1)d topological gauge model, I show that there exists distinct parametrisations labelled by gapped boundary conditions of its ground state subspace in the form of tensor networks. Two such parametrisations fulfill symmetry conditions w.r.t. operators encoded into the Morita equivalent fusion 2-categories \(\mathsf{2Vec}_G\) and \(\mathsf{2Rep}(G)\), respectively. This is the electromagnetic duality of (3+1)d topological gauge models. In the context of (2+1)d quantum lattice models, this construction infers that gauging a \(G\)-symmetry results in a model with a \(\mathsf{2Rep}(G)\)-symmetry.
DALL·E 3, Knots I, 2023

String-like excitations in (3+1)d gauge models of topological phases

We propose a classification and a characterisation of string-like excitations in gauge models of topological phases. Our derivations rely on a generalization of the so-called "tube algebra" approach, which consists in revealing the algebra, or categorification thereof, underlying the excitations and derive the elementary excitations as the corresponding simple modules. In particular, we find that these string-like excitations are organized into 2-category that is equivalent to the monoidal center of the input fusion 2-category. We further formalise the idea that closing string-like excitations produces loop-like ones.
Mondrian, Composition A, 1923

Computing the renormalisation group flow of \(\phi^4\) theory with tensor networks

Regularising space into a fine-grained lattice and discretising the scalar field, the partition function of 2d \(\phi^4\) quantum field theory can be written down as a tensor network. Computing the partition function then boils down to contracting the tensor network. In 2017, M. Hauru, S.Mizera & I introduced a simple algorithm coined "gilt-TNR" that performs such a contraction approximately and, as a by-product, computes the renormalisation group flow of the theory in the space of tensors. Applied to \(\phi^4\) theory, we obtained at the time the best estimate for the criticial coupling of the theory in the continuum limit.


You can find additional information on the links below. Feel free to reach out by email.