Séminaires du LPTMC

Salle 523, couloir 12-13, 5è étage

Gauge-Like Symmetries, Dimensional Reduction, and Dualities: From Topological Order to Constrained Dynamics

I will present a unified view of dualities and symmetries. We will start by reviewing how conventional dualities help identify topological defects in Ising, XY, and continuum elasticity theories and demonstrate how gauge invariance and conservation laws enforce kinematic glide for dislocations in elastic media. Next we will turn to general d-dimensional gauge-like symmetries which include "higher form" and "subsystem" symmetries. In quantum and classical systems, these structures can lead to dimensional reduction, constrained dynamics, and forms of fractionalization and topological order. After introducing a generalization of Elitzur's theorem, I will show how the delicate confluence of symmetries and system geometry may lead to topological degeneracies and holographic entropies (associated with exponential in boundary area multiplicities). We will introduce a general (bond-algebraic) framework for dualities which we will employ to illustrate that several models that harbor topological order as well as square lattice compass variants of the Hubbard model exhibit exact three-dimensional classical Ising transitions and further use these dualities to compute the free energy of various other systems including the fracton ``X-cube'' model. We will finally turn to to "non-invertible" symmetries and provide a generalization of Wigner theorem which will illustrate that all such symmetries may be recast as invertible ones, with the bond algebra approach providing a unifying tool. Time permitting, we will show why duality transformations are generally conformal and use this property to derive new relations in combinatorial geometry.

Salle 523, couloir 12-13, 5è étage

Quantum Thermalization via Travelling Waves in Isolated and Open Quantum Systems

Isolated quantum many-body systems which thermalize under their own dynamics are expected to act as their own thermal baths [1], thereby losing memory of initial conditions and bringing their local subsystems to thermal equilibrium. Here [2], we show that the infinite- dimensional limit of a quantum lattice model, as described by dynamical mean-field theory (DMFT), provides a natural framework to understand this self-consistent thermalization process. Using the Fermi-Hubbard model as a working example, we demonstrate that the emergence of a self-consistent bath occurs via a sharp thermalization front, moving ballistically and separating the initial condition from the long time thermal fixed point (Fig. 1). We characterize the full DMFT dynamics through an effective temperature for which we derive a traveling wave equation of the Fisher-Kolmogorov-Petrovsky-Piskunov type [3]. We extend our results in order to study the shape of the front and its velocity in open dissipative fermionic systems by integrating DMFT into the Lindblad Master Equation formalism. We show that thermalization under open quantum system dynamics is qualitatively different from the closed-system case. In particular, the thermalization front is strongly modified, a signature of the irreversibility of open-system dynamics [4]

Salle 523, couloir 12-13, 5è étage

First passages, survival probabilities & higher-dimensional convex hulls

First I will present joint work with B. de Bruyne and S. Redner, on first-passage resetting, where the resetting of a random walk to a fixed position is triggered by a first-passage event of the walk itself. We define an optimization problem that is controlled by first-passage resetting: a cost is incurred whenever the particle is reset and a reward is obtained while the particle stays near the reset-trigger point. We derive the condition to optimize the net gain in this system, namely, the reward minus the cost. I will also talk about an extension of first-passage resetting into a minimalist dynamical model of wealth evolution and wealth sharing among N agents.

Second, I will present joint work with G. Uribe Bravo and D. Zaporozhets. We focus on the convex hull of a single multidimensional random walk, with i.i.d. steps taken from any symmetric, continuous distribution. We investigate the persistence of vertices and faces on the hull. In particular we show that the corresponding distributions are universal, and follow three regimes closely linked to the Sparre Andersen theorem for one dimensional random walks.

Third, time-permitting (hence, probably not...), I will turn to the convex hull of several multidimensional Gaussian random walks. Explicit formulas for the expected volume and expected number of faces are derived in terms of the Gaussian persistence probabilities. Special cases include the already known results about the convex hull of a single Gaussian random walk and the d-dimensional Gaussian polytope.

References:

de Bruyne, B., R.-F., J., Redner, S. (2020). Phys. Rev. Letters, 125(5), 050602

de Bruyne, B., R.-F., J., Redner, S. (2021). J. Stat. Mech., 2021(10), 103405

R.-F., J., Zaporozhets, D. (2024). J. Math. Sc., 281(1)

R.-F., J., Uribe Bravo, G., Zaporozhets, D. to appear (2026)

Salle 523, couloir 12-13, 5è étage

Integrable Dynamics and Thermalization in the Quantum O(n) Model at Large n

The quantum O(n) model has long served as a valuable framework for studying both equilibrium and dynamical properties of quantum many-body systems. In this talk, we investigate its non-equilibrium dynamics following a quantum quench in the large-n limit. While the model is known to be tractable in this regime, we show that it is in fact integrable - with integrals of motions stemming from that of the classical Neumann model - thus enabling a complete analytical solution of its dynamics. This integrability reveals a synchronization mechanism that gives rise to persistent oscillations, interpretable as Higgs modes localized at the edge of the spectral band. We further demonstrate that the long-time behavior is governed by a Generalized Gibbs Ensemble (GGE), in contrast to previous expectations, and we obtain exact critical exponents differing from those commonly reported. Remarkably, integrability persists even in the presence of long-range couplings, allowing us to explore the crossover between mean-field and genuinely many-body regimes in terms of parametric Floquet resonances of the microscopic degrees of freedom.

Salle 523, couloir 12-13, 5è étage

Complex interactions in and out of equilibrium

One of the main challenges in the modeling of biological systems is that their physical behavior at all scales is
dictated by intricate interactions between many different complex objects. In this talk, I will present theoretical
results on two different systems where complex interactions play a key role, one equilibrium and the other active.

I will first discuss the equilibrium self-assembly of proteins, which can be seen as particles with short-range
anisotropic interactions. Strikingly, proteins with vastly different physico-chemical properties tend to form into
similar fibrous pathological aggregates. By performing lattice Monte-Carlo simulations of three-dimensional particles, I
will show that complex anisotropic iteractions lead to a great morphological diversity in the resulting assemblies. In
particular, many choices of interactions lead to the formation of fibers, which are found to result from geometrical
frustration. On the other hand, I will also demonstrate that anisotropy is a useful design tool for controlling the size
and shape of equilibrium aggregates.

In a second part, I will discuss the self-organization of mixtures of enzyme-like active particles. As opposed to the
previous system, these objects are intrinsically out of equilibrium, and develop isotropic, long-ranged, non-reciprocal
interactions. By using a combination of linear stability analysis and Brownian dynamics simulations, I will show that
catalytically active particles can self-organize into droplet-like structures. My focus will be on the case where
different species of enzymes participate in a biochemical reaction network. This different type of complexity, which
stems from the existence of an intricate interaction network between different species instead of structural anisotropy,
can be an intrinsic driver of self-organization and lead to novel collective dynamics.

Salle 523, couloir 12-13, 5è étage

Scaling of many-body localization transitions: Correlations and dynamics in Fock space and real space

Many-body localization (MBL) is a remarkable phenomenon where interacting quantum systems fail to thermalize due to disorder. Despite two decades of intense theoretical and numerical work, there is still no clear consensus on whether a true 1D MBL phase exists in the thermodynamic limit, or whether it eventually gives way to slow thermalization.

After a broad introduction to the current open questions surrounding MBL, I will discuss recent results [1] on how MBL transitions scale with system size in several different disordered spin-½ models. By representing these models as effective tight-binding problems in Fock space—where “sites’’ correspond to many-body basis states and “hoppings’’ to interactions—we can explicitly identify the role of correlations between Fock-space energies and couplings in the onset of localization and the breakdown of ergodicity. Comparing models with and without such correlations (1D spin chains, quantum dot with all-to-all interactions, and the quantum random energy model) reveals strikingly different scaling behaviors for the critical disorder strength and transition width, which we predicted analytically and verified numerically. Finally, I will show how real-space dynamical probes that are accessible to modern simulators, such as the time evolution of the “generalized” imbalance, also capture the features of the transition from the Fock-space perspective, and allow us to construct consistent finite-size phase diagrams, in full agreement with spectral observables [2].

[1] T. Scoquart, I. Gornyi and A. Mirlin, Role of Fock-space correlations in many-body localization, Phys. Rev. B 109, 214203, (2024)
[2] T. Scoquart, I. Gornyi and A. Mirlin, Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space, Phys. Rev. B 112, 064203 (2025)

Salle 523, couloir 12-13, 5è étage

The "Mode-Shell" correspondence, a unifying concept in topological physics

In quantum or classical wave systems, some properties of wave systems are known to be topologically protected. Due to their increased robustness, such properties have attracted much interest in the past decades.

The most studied case is the existence of unidirectional edge states in the quantum Hall effect and, more generally, the existence of protected states at the edges of topologically insulators. An important result is then the bulk-edge correspondence that links the existence of topological edge states to a topological index defined in the volume of the material.

This is not the only case studied in topological physics and different, yet similar, results have been obtained for topological semimetals, higher order insulators or continuous wave systems. In this talk I will explain how all these results can be understood in a unifying theory using the mode-shell correspondence formalism which relates the existence of isolated topological modes in phase space, to a topological invariant defined in the surface which encloses these modes in phase space. Invariant that reduces to Chern or winding numbers in the semiclassical limit.

Mode-shell correspondence, a unifying phase space theory in topological physics
[1] Part I: Chiral number of zero-modes https://www.scipost.org/10.21468/SciPostPhys.17.2.060
[2] Part II: Higher-dimensional spectral invariants https://arxiv.org/abs/2501.13550