LABORATOIRE DE PHYSIQUE ET MODELISATION DES MILIEUX CONDENSES

The renormalization group is an established approach to study quantum many-body systems, and this applies especially to one of its modern implementations known as the functional renormalization group (fRG). In particular, the fRG constitutes a flexible and unbiased tool for the study of competing orders. In this talk, I will outline recent progress in this direction for correlated electron systems. To this end, I will first discuss the competition between antiferromagnetism, charge density waves and superconductivity in the 2D Hubbard model, thus making a connection with high-temperature superconductors. The special role of bosonization methods will be emphasized along the way. I will also show how the fRG can be combined with dynamical mean-field theory to treat strongly interacting regimes, with a focus on d-wave superconductivity. As a next step, I will increase the complexity of the model by including non-local interactions and discuss unconventional superconductivity in an extended Hubbard model with a connection to moiré materials. Special consideration will also be given to the treatment of retarded interactions with electron-phonon couplings. Finally, I will highlight recent fRG studies of quantum criticality in Dirac materials, with a connection to graphene.

When subjected to a strong magnetic field, electrons on a two-dimensional lattice acquire a fractal energy spectrum called Hofstadter's butterfly. In addition to its unique recursive structure, the Hofstadter butterfly is intimately linked to non-trivial topological orders, hosting a cascade of ground states characterized by non-zero topological invariants. These states, called Chern insulators, are usually understood as replicas of the ground states of the quantum Hall effect, with electrical and thermal conductances that should be quantized, reflecting their topological order. The Hofstadter butterfly is now commonly observed in van-der-Waals heterostructures-based moiré superlattices. However, its thermal properties, particularly the quantized heat flow expected in the Chern insulators, have not been investigated, potentially questioning their similarity with standard quantum Hall states. Here we probe the heat transport properties of the Hofstadter butterfly, obtained in a graphene / hexagonal boron nitride moiré superlattice. We observe a quantized heat flow, uniquely set by the topological invariant, for all investigated states of the Hofstadter butterfly: quantum Hall states, Chern insulators, and even symmetry-broken Chern insulators emerging from strong electronic interactions. Our work firmly establishes the universality of the quantization of heat transport and its intimate link with topology.

A. Zhang, et al., arXiv:2601.05694 (2026)

There are multiple measures of multipartite entanglement — including entanglement in thermal mixtures — currently used to study many-body interacting systems. Recently, Quantum Fisher Information has been proposed as a multipartite entanglement measure that can be connected to experimentally accessible observables. In this talk, I will present our recent findings about a one-to-one correspondence between two-point correlators and a certain general class of Heisenberg-like Hamiltonians and wavefunctions. This is a foundation of our claim that a mapping from finite-temperature observables to any entanglement measure exists for such systems. Furthermore, I will present our results of training a convolutional neural network (CNN) to recognize and predict the entanglement for one-dimensional anisotropic XY and XYZ models, which exhibit an entanglement transition. From our preliminary results we found that entanglement can be accurately predicted by a CNN using both static and dynamical correlators, even when the network is trained on only a fraction of the full dataset or on data from a different system than the one used for prediction. Specifically, when trained on observables from an anisotropic XY model, accurate predictions can be achieved using only about 3% (6%) of the data when employing dynamical two-point correlators (structure factors) for learning.

With the scaling of quantum technologies to many separate material quantum components, we may have to couple these systems by propagating quantum radiation, in the form of light, microwaves or phonons. There are, however, rather fundamental obstacles to the treatment of propagation of quantum radiation and its interaction with matter. These obstacles include the general multimode character of propagating fields and the duration and spatial extent of useful light and microwave pulses. The talk will review a recent theoretical approach to deal theoretically with these obstacles, and it will present examples of new, unforeseen, possibilities for easy preparation and manipulation “on the fly” of quantum states of light and matter.