arXiv subjects

Gabriel Lemarié

Publications and source records attributed to Gabriel Lemarié.

At least 19 recordsLinked to original sources

arXiv2026

Connecting finite-size scaling and renormalization-group flows in Anderson localization on random graphs

We investigate the relation between two complementary descriptions of the Anderson transition on small-world random graphs: finite-size scaling of eigenfunction moments and renormalization-group (RG) flows of multifractal dimensions $D_q$. The RG flows recover the qualitative structure previously reported for the information dimension $D_1$, while their extension to other $D_q$ with smaller moment orders $q<1/2$ confirms the strongly multifractal nature of the localized phase characterized by a clear separation between multifractal and localized behaviors at strong disorder. On the other hand, we show that we can construct another beta function characterizing the flow of eigenfunction moments, whose collapse onto a single function across different disorder strengths provides a clear confirmation of single-parameter scaling property. These results indicate that the family of RG trajectories observed for the information dimension $D_1$ need not imply two-parameter scaling and Kosterlitz-Thouless like critical behavior. To characterize these properties, one should consider different observables, such as large $q>1/2$ and small $q<1/2$ eigenfunction moments, which are associated with distinct critical behaviors, in particular different critical exponents.

cond-mat.dis-nn↗

arXiv2026

Enhanced Density Fluctuations Near a Disordered Chiral Topological Transition

The universal statistics of density fluctuations of localized quantum states may offer unprecedented opportunities to probe and understand quantum transport in connection with dimensionality, coherence, symmetry and disorder. To date, the possible role of topological phase transitions in the fluctuation statistics is not studied yet. Using a Su-Schrieffer-Heeger chain subject to off-diagonal disorder (so that chiral symmetry is preserved), this work investigates how a disorder driven topological phase transition impacts on the spatial fluctuations of the logarithmic wave-packet density $\ln P(r)$ at distance $r$ from the initial excitation. Away from the transition, in both topological and trivial localized phases, the standard deviation follows the conventional one-dimensional scaling $σ[\ln P(r)]\sim r^θ$ with $θ\simeq 1/2$. Near the transition, however, the fluctuation growth is enhanced: the fitted exponent $θ$ increases above $1/2$ in a nonmonotonic manner before returning close to $1/2$ at criticality. We interpret this behavior from the energy-resolved density of states and localization length. Near the transition, several energy sectors carry appreciable spectral weight and exhibit competitive decay rates, preventing a single localization scale from dominating the accessible wave-packet tail and thereby enhancing the fluctuations of $\ln P(r)$. Our results establish wave-packet fluctuation statistics as a dynamical diagnostic of disordered chiral topological transitions and motivate broader studies of fluctuation phenomena in disordered topological quantum systems.

cond-mat.dis-nn↗

arXiv2026

Many-body dynamical localization in Fock space

We investigate the emergence of many-body dynamical localization (MBDL) in the Fock space of an interacting two-mode bosonic system subject to periodic driving. Using a mapping to the paradigmatic kicked-top model, we analyze the interplay between classical chaotic diffusion and quantum interference effects. While the mean-field (classical) dynamics exhibits bounded ergodic diffusion along the population imbalance axis, the quantum dynamics reveals strong suppression of transport in Fock space, in close analogy with Anderson localization in disordered lattices. We characterize the localization length, its scaling with particle number and driving parameters, and reveal the spectral crossover from random-matrix to Poisson statistics as the many-body ensemble localizes. We highlight the connection between MBDL and discrete time crystals. Our findings offer a promising avenue to study the Anderson transition in Fock space.

cond-mat.quant-gas↗

arXiv2026

Symmetry-Induced Logarithmic Relaxation in the Quantum Kicked Rotor

We study the effect of discrete symmetries on coherent multiple scattering in the quantum kicked rotor. When the initial momentum is set to zero -- as in recent Bose-Einstein condensate experiments -- the effective pseudo-disorder becomes even under momentum inversion. The resulting discrete mirror symmetry of the dynamics profoundly alters spectral correlations: it generates quasi-degenerate Floquet doublets localised at opposite momenta, whose exponentially small splittings produce a hierarchy of exponentially large dynamical timescales. The coherent backscattering and forward-scattering peaks then exhibit a striking non-monotonic evolution and strongly asymmetric contrasts, followed by an exceptionally slow logarithmic relaxation toward a common asymptotic value -- a hallmark of glassy dynamics, here emerging in a fully coherent quantum system. That such archetypal glass-like behaviour arises from a single discrete symmetry constraint reveals an unexpected and deep connection between quantum coherence and slow relaxation phenomena.

cond-mat.dis-nn↗

arXiv2025

Kardar-Parisi-Zhang and glassy properties in 2D Anderson localization: eigenstates and wave packets

Despite decades of research, the universal nature of fluctuations in disordered quantum systems remains poorly understood. Here, we present extensive numerical evidence that fluctuations in two-dimensional (2D) Anderson localization belongs to the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) universality class. In turn, by adopting the KPZ framework, we gain fresh insight into the structure and phenomenology of Anderson localization itself. We analyze both localized eigenstates and time-evolved wave packets, demonstrating that the fluctuation of their logarithmic density follows the KPZ scaling. Moreover, we reveal that the internal structure of these eigenstates exhibits glassy features characteristic of the directed polymer problem, including the emergence of dominant paths together with pinning and avalanche behavior. Localization is not isotropic but organized along preferential branches of weaker confinement, corresponding to these dominant paths. For localized wave packets, we further demonstrate that their spatial profiles obey a stretched-exponential form consistent with the KPZ scaling, while remaining fully compatible with the single-parameter scaling (SPS) hypothesis, a cornerstone of Anderson localization theory. Altogether, our results establish a unified KPZ framework for describing fluctuations and microscopic organization in 2D Anderson localization, revealing the glassy nature of localized states and providing new understanding into the universal structure of disordered quantum systems.

cond-mat.dis-nn↗

arXiv2025

Extreme statistics as a probe of the superfluid to Bose-glass Berezinskii-Kosterlitz-Thouless transition

Recent studies of delocalization-localization transitions in disordered quantum chains have highlighted the role of rare, chain-breaking events that favor localization, in particular for high-energy eigenstates related to many-body localization. In this context, we revisit the random-field XXZ spin-1/2 chain at zero temperature with ferromagnetic interactions, equivalent to interacting fermions or hard-core bosons in a random potential with attractive interactions. We argue that localization in this model can be characterized by chain-breaking events, which are probed by the extreme values of simple local observables, such as the on-site density or the local magnetization, that are readily accessible in both experiments and numerical simulations. Adopting a bosonic language, we study the disorder-induced Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition from superfluid (SF) to Bose glass (BG), and focus on the strong disorder regime where localization is driven by weak links. Based on high-precision density matrix renormalization group simulations, we numerically show that extreme local densities accurately capture the BKT transition, even for relatively short chains ranging from a few dozen to a hundred sites. We also discuss the SF-BG transition in the weak disorder regime, where finite-size effects pose greater challenges. Overall, our work seeks to establish a solid foundation for using extreme statistics of local observables, such as density, to probe delocalization-localization transitions in disordered quantum chains, both in the ground state and at high energy.

cond-mat.dis-nn↗

arXiv2025

Engineering many-body quantum Hamiltonians with non-ergodic properties using quantum Monte Carlo

We present a computational framework to identify Hamiltonians of interacting quantum many-body systems that host non-ergodic excited states. We combine quantum Monte Carlo simulations with the recently proposed eigenstate-to-Hamiltonian construction, which maps the ground state of a specified parent Hamiltonian to a single non-ergodic excited state of a new derived Hamiltonian. This engineered Hamiltonian contains non-trivial, systematically-obtained, and emergent features that are responsible for its non-ergodic properties. We demonstrate this approach by applying it to quantum many-body scar states where we discover a previously unreported family of Hamiltonians with spatially oscillating spin exchange couplings that host scar-like properties, including revivals in the quantum dynamics, and towers in the inverse participation ratio; and to many-body localization, where we find a two-dimensional Hamiltonian with correlated disorder that exhibits non-ergodic scaling of the participation entropy and inverse participation ratios of order unity. The method can be applied to other known ground states to discover new quantum many-body systems with non-ergodic excited states.

cond-mat.str-el↗

arXiv2025

2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes

We challenge two foundational principles of localization physics by analyzing conductance fluctuations in two dimensions with unprecedented precision: (i) the Thouless criterion, which defines localization as insensitivity to boundary conditions, and (ii) that symmetry determines the universality class of Anderson localization. We reveal that the fluctuations of the conductance logarithm fall into distinct sub-universality classes inherited from Kardar-Parisi-Zhang (KPZ) physics, dictated by the lead configurations of the scattering system and unaffected by the presence of a magnetic field. Distinguishing between these probability distributions poses a significant challenge due to their striking similarity, requiring sampling beyond the usual threshold of $\sim 10^{-6}$ accessible through independent disorder realizations. To overcome this, we implement an importance sampling scheme - a Monte Carlo approach in disorder space - that enables us to probe rare disorder configurations and sample probability distribution tails down to $10^{-30}$. This unprecedented precision allows us to unambiguously differentiate between KPZ sub-universality classes of conductance fluctuations for different lead configurations, while demonstrating the insensitivity to magnetic fields.

cond-mat.dis-nn↗

arXiv2025

Coherent backscattering and coherent forward scattering effects in variations of the random quantum kicked rotor

We investigate coherent multiple scattering effects in the random quantum kicked rotor model. By changing the starting time of the Floquet period, two new classes of models can be introduced that exhibit similar interference structures. For one of the two classes, these structures appear on top of a non-trivial background, which we describe in detail. Its origin is identified and an approximate analytical formula is proposed. The asymptotic contrast profile, as well as the height of the coherent backscattering and the coherent forward scattering peaks, are also analyzed. Our findings are relevant to provide an interpretation of cold atom experiments aiming at observing such interference effects with matter waves.

quant-ph↗

arXiv2025

Critical Dynamics of the Anderson Transition on Small-World Graphs

The Anderson transition on random graphs draws interest through its resemblance to the many-body localization (MBL) transition with similarly debated properties. In this Letter, we construct a unitary Anderson model on Small-World graphs to characterize long time and large size wave-packet dynamics across the Anderson transition. We reveal the logarithmically slow non-ergodic dynamics in the critical regime, confirming recent random matrix predictions. Our data clearly indicate two localization times: an average localization time that diverges, while the typical one saturates. In the delocalized regime, the dynamics are initially non-ergodic but cross over to ergodic diffusion at long times and large distances. Finite-time scaling then allows us to characterize the critical dynamical properties: the logarithm of the average localization time diverges algebraically, while the ergodic time diverges exponentially. Our results could be used to clarify the dynamical properties of MBL and could guide future experiments with quantum simulators.

cond-mat.dis-nn↗

arXiv2025

Universal fluctuations of localized two interacting particles in one dimension

We investigate the universal fluctuations of localized wavefunction in the Fock space of two interacting particles in one-dimensional disordered systems, focusing on the interplay between random potentials and random long-range interactions. By mapping the system onto a directed polymer problem, we show that random potentials alone produce correlated energies for the sites in the Fock space, giving rise to the fluctuation growth exponent 1/2. Introducing random long-range interactions alters these correlations and drives the system's fluctuations into the Kardar-Parisi-Zhang universality class in (1+1)D with the exponent 1/3. To validate the universality of the observed fluctuation scaling, we study a complex directed polymer model with competing point and columnar disorder. Our results confirm that columnar disorder corresponds to on-site energies in the Fock space from the random potentials, while point disorder models the effects of random long-range interactions between the two particles. These findings provide new insights into the Fock-space perspective for examining disordered quantum many-body systems, and emphasize the critical role of disorder structure in determining the universality class of fluctuations in localized quantum systems.

cond-mat.dis-nn↗

arXiv2024

Describing the critical behavior of the Anderson transition in infinite dimension by random-matrix ensembles: logarithmic multifractality and critical localization

Due to their analytical tractability, random matrix ensembles serve as robust platforms for exploring exotic phenomena in systems that are computationally demanding. Building on a companion letter [arXiv:2312.17481], this paper investigates two random matrix ensembles tailored to capture the critical behavior of the Anderson transition in infinite dimension, employing both analytical techniques and extensive numerical simulations. Our study unveils two types of critical behaviors: logarithmic multifractality and critical localization. In contrast to conventional multifractality, the novel logarithmic multifractality features eigenstate moments scaling algebraically with the logarithm of the system size. Critical localization, characterized by eigenstate moments of order $q>1/2$ converging to a finite value indicating localization, exhibits characteristic logarithmic finite-size or time effects, consistent with the critical behavior observed in random regular and Erdös-Rényi graphs of effective infinite dimensionality. Using perturbative methods, we establish the existence of logarithmic multifractality and critical localization in our models. Furthermore, we explore the emergence of novel scaling behaviors in the time dynamics and spatial correlation functions. Our models provide a valuable framework for studying infinite-dimensional quantum disordered systems, and the universality of our findings enables broad applicability to systems with pronounced finite-size effects and slow dynamics, including the contentious many-body localization transition, akin to the Anderson transition in infinite dimension.

cond-mat.dis-nn↗

arXiv2023

Quantum logarithmic multifractality

Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing the Anderson transition. In marked contrast to conventional multifractal critical properties observed at finite-dimensional Anderson transitions or scale-invariant second-order phase transitions, in the presence of logarithmic multifractality, eigenstate statistics, spatial correlations, and wave packet dynamics can all exhibit scaling laws which are algebraic in the logarithm of system size or time. Our findings offer crucial insights into strong finite-size effects and slow dynamics in complex systems undergoing the Anderson transition, such as the many-body localization transition.

cond-mat.dis-nn↗

arXiv2023

Absence of a direct metal to Mott insulator transition for disordered interacting fermions on the Cayley tree

Interacting fermions in the presence of disorder pose one of the most challenging problems in condensed matter physics, primarily due to the absence of accurate numerical tools. Our investigation delves into the intricate interplay between interaction-induced Mott insulation and disorder-driven Anderson localization in the Hubbard model subjected to a random potential. On the Cayley tree, the application of statistical dynamical mean-field theory proves adept at discerning among a metal and the two distinct insulators, Anderson or Mott. Our comprehensive analysis, accounting for subtle yet potent finite-size effects and fluctuations, yields a noteworthy finding: in the presence of disorder, we consistently observe an intervening Anderson-localized regime between the metallic and Mott insulator states. This observation intriguingly mirrors scenarios witnessed in dirty Bosons, where an insulating Bose glass phase consistently emerges between the superfluid and Mott phases.

cond-mat.str-el↗

arXiv2023

Kardar-Parisi-Zhang Physics in the Density Fluctuations of Localized Two-Dimensional Wave Packets

We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit an algebraic scaling with distance characterized by an exponent of $1/3$, and a Tracy-Widom probability distribution of the fluctuations. Additionally, within a directed polymer picture of KPZ physics, we identify the dominant contribution of a directed path to the wave packet density and find that its transverse fluctuations are characterized by a roughness exponent $2/3$. Leveraging on this connection with KPZ physics, we verify that an Anderson localized wave packet in 2D exhibits a stretched-exponential correction to its well-known exponential localization.

cond-mat.dis-nn↗

arXiv2022

Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree

We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant and algebraically vanishing boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.

cond-mat.dis-nn↗

arXiv2022

Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization

The Anderson transition in random graphs has raised great interest, partly because of its analogy with the many-body localization (MBL) transition. Unlike the latter, many results for random graphs are now well established, in particular the existence and precise value of a critical disorder separating a localized from an ergodic delocalized phase. However, the renormalization group flow and the nature of the transition are not well understood. In turn, recent works on the MBL transition have made the remarkable prediction that the flow is of Kosterlitz-Thouless type. Here we show that the Anderson transition on graphs displays the same type of flow. Our work attests to the importance of rare branches along which wave functions have a much larger localization length $ξ_\parallel$ than the one in the transverse direction, $ξ_\perp$. Importantly, these two lengths have different critical behaviors: $ξ_\parallel$ diverges with a critical exponent $ν_\parallel=1$, while $ξ_\perp$ reaches a finite universal value ${ξ_\perp^c}$ at the transition point $W_c$. Indeed, $ξ_\perp^{-1} \approx {ξ_\perp^c}^{-1} + ξ^{-1}$, with $ξ\sim (W-W_c)^{-ν_\perp}$ associated with a new critical exponent $ν_\perp = 1/2$, where $\exp( ξ)$ controls finite-size effects. The delocalized phase inherits the strongly non-ergodic properties of the critical regime at short scales, but is ergodic at large scales, with a unique critical exponent $ν=1/2$. This shows a very strong analogy with the MBL transition: the behavior of $ξ_\perp$ is identical to that recently predicted for the typical localization length of MBL in a phenomenological renormalization group flow. We demonstrate these important properties for a smallworld complex network model and show the universality of our results by considering different network parameters and different key observables of Anderson localization.

cond-mat.dis-nn↗

arXiv2022

Superfluidity vs prethermalisation in a nonlinear Floquet system

We show that superfluidity can be used to prevent thermalisation in a nonlinear Floquet system. Generically, periodic driving boils an interacting system to a featureless infinite temperature state. Fast driving is a known strategy to postpone Floquet heating with a large but always finite boiling time. In contrast, using a nonlinear periodically-driven system on a lattice, we show the existence of a continuous class of initial states which do not thermalise at all. This absence of thermalisation is associated to the existence and persistence of a stable superflow motion.

cond-mat.quant-gas↗