
chair: Ilya Gruzberg

09:00  09:35

Radu Chicireanu
(Université de Lille)
Observation of Quantum Criticality of a FourDimensional Phase Transition
Understanding how a system’s behavior extrapolates beyond the dimensionality of our 3D world is a fundamental question throughout physics – spanning from the pursuit of unification theories to the exploration of exotic materials and into the realms of critical phenomena. In statistical physics, the strength of the fluctuations is very sensitive to the dimensionality, which in turn plays a key role in the existence and nature of phase transitions. Most often, lowdimensional systems often exhibit suppression of phase transitions, while highdimensional systems tend to display simpler, meanfieldlike behavior. In a few outstanding cases, among which the celebrated Anderson localizationdelocalization transition in disordered media, criticality has been predicted to remain highly nontrivial even in dimensions larger than three – posing great theoretical challenges to the existing frameworks. In this work, using a periodicallydriven ultracold atomic gas to engineer
both disorder and synthetic dimensions, we experimentally observe and investigate a phase transition between (dynamically) localized and delocalized phases. Our results clearly exhibit three fundamental characteristics that define the specific 4D nature of the observed phase transition: 1) the relevant observables perfectly follow the d=4 critical scale invariance, 2) the measured critical exponents are in excellent agreement with numerical predictions of the 4D Anderson transition and, 3) they show good agreement with Wegner’s relation in 4D. These results open a new paradigm for experimentally exploring complex critical phenomena, and physical theories in general, in higher dimensions.

09:35  10:10

Marcel Filoche
(ESPCI Paris)
The deep structure of the Anderson transition phase diagram
The structure of the phase diagram of localization in the energydisorder plane, for random tightbinding Hamiltonians exhibits several well known properties: below dimension $d=2$, all eigenfunctions are localized for nonvanishing disorder. Above $d=2$, a delocalized phase appears separated from the localized phase by a transition line called the “mobility edge,” predicted by the socalled selfconsistent theory of localization in the case of uniform disorder. We will show that, with a closer examination, a more complicated structure emerges in which several types of mechanisms interplay to give rise to this diagram and its localization/delocalization transition. In particular, we will present the latest advances obtained using the localization landscape theory.

10:10  10:35

Serguei Skipetrov
(Université GrenobleAlpes & CNRS)
Anderson localization of light in three dimensions
Previous theoretical research demonstrated that longitudinal electromagnetic fields impede Anderson localization of light in threedimensional (3D) random ensembles of resonant pointlike scatterers [1,2]. At the same time, experimental efforts to observe Anderson localization of light in 3D were unsuccessful for various reasons (see Ref. 3 for a summary). Our recent numerical simulations made possible by a new, highly efficient combination of software and hardware, demonstrate that Anderson localization of light is impossible in large random ensembles of overlapping dielectric spheres, suggesting a plausible explanation for the failure of previous experiments [4]. Motivated by the work on the detrimental role of longitudinal electromagnetic fields [1,2], we propose to look for Anderson localization of light in porous conducting (i.e., metallic) structures where longitudinal fields are suppressed. Our numerical results demonstrate that indeed, transmission of light through such structures exhibits signatures expected for Anderson localization: nonexponential decay of the timedependent transmission, arrested expansion of the diffusive halo, enhanced fluctuations in the spectrum of light, etc. [4]. We suggest that future experimental and theoretical research on Anderson localization of light in 3D should focus on metallic structures with random, percolating pores.
1. S.E. Skipetrov & I.M. Sokolov, Absence of Anderson localization of light in a random ensemble of point scatterers, Phys. Rev. Lett. 112, 023905 (2014)
2. B.A. van Tiggelen & S.E. Skipetrov, Longitudinal modes in diffusion and localization of light, Phys. Rev. B 103, 174204 (2021)
3. S.E. Skipetrov & J.H. Page, Red light for Anderson localization, New J. Phys. 18, 021001 (2016)
4. A. Yamilov, S.E. Skipetrov, T.W. Hughes, M. Minkov, Z. Yu, & H. Cao, Anderson localization of electromagnetic waves in three dimensions, Nature Physics 19, 1308 (2023)

10:35  11:05

coffee break

11:05  11:40

Tomi Ohtsuki
(Sophia University)
Localization in quasiperiodic systems
A quasiperiodic system is an intermediate state between periodic and disordered systems with a unique delocalizationlocalization transition driven by the quasiperiodic potential (QP). One of the intriguing questions is whether the universality class of the Anderson transition (AT) driven by QP is similar to that of the AT driven by the random potential in the same symmetry class. Here, we study the critical behavior of the ATs driven by QP in the threedimensional (3D) Anderson model, the Peierls phase model, and the Ando model, which belong to the WignerDyson symmetry classes. The localization length and twoterminal conductance have been calculated using the transfermatrix method, and we argue that their error estimations in statistics suffer from the correlation of QP. With the correlation under control, the critical exponents ν of the ATs driven by QP are estimated by the finitesize scaling analysis of conductance, and they are consistent with the exponents ν of the ATs driven by the random potential. We also find that a convolutional neural network trained by the localized/delocalized wave functions in a disordered system predicts the localization/delocalization of the wave functions in quasiperiodic systems. Our numerical results strongly support the idea that the universality classes of the ATs driven by QP and the random potential are similar in the 3D WignerDyson symmetry classes. We will also comment on the hyperuniformity in lowdimensional systems.
[1] X. Luo and T. Ohtsuki, Phys. Rev. B 106, 104205 (2022).
[2] S. Sakai, R. Arita and T. Ohtsuki, Phys. Rev. B 105, 054202 (2022), Phys. Rev. Res. 4, 033241 (2022).

11:40  12:15

Jonas Karcher
(Princeton University)
Generalized multifractality and (violation of) conformal invariance at Anderson transitions
We explore the concept of generalized multifractality (GMF), which characterizes eigenstate fluctuations and correlations in disordered systems.
Utilizing the nonlinear sigma model formalism, we construct purescaling composite operators and their positive eigenfunction observable counter part,
enabling the efficient numerical determination of scaling exponents. These exponents determine the renormalization group (ir)relevance of interactions.
Further, recent findings (PRL 131, 266401) show that conformal invariance leads to the generalized parabolicity of the GMF spectrum
(i.e., proportionality to eigenvalues of the quadratic Casimir operator).
On the one hand, we demonstrate that the fixedpoint theory of the spin quantum Hall (SQH) transition violates conformal invariance,
using a mapping to classical percolation for a specific set of GMF observables, and show analytically and numerically that generalized parabolicity does not hold.
On the other hand, we examine disordered 3D topological superconductors, whose surface states in the bulk gap are described by WessZumino models and exhibit full conformal invariance.
These results indicate that the presence of full conformal invariance in Anderson critical systems depends on the (topological) universality class of the transition.

12:15  12:40

Sen Mu
(National University of Singapore)
Anderson localization and KardarParisiZhang universality class
We identify the key features of KardarParisiZhang (KPZ) universality class in the fluctuations of the wave density logarithm in a twodimensional 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 TracyWidom 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 two dimensions exhibits a stretched exponential correction to its wellknown exponential localization.
Ref: Phys. Rev. Lett. 132, 046301 (2024)

12:40  14:30

lunch and discussions


chair: Angelo Russomanno

14:30  15:05

Gabriel Lemarié
(National University of Singapore)
Logarithmic Multifractality
In this talk, I will present our recent findings on the Anderson transition in effectively
infinitedimensional systems, revealing an exotic critical behavior termed ”logarithmic
multifractality” [1,2]. Unlike the conventional multifractal properties observed at finitedimensional Anderson transitions, logarithmic multifractality features eigenstate statistics, spatial correlations, and wave packet dynamics that exhibit scaling laws algebraic in the logarithm of system size or time. I will compare this critical behavior with that we found in smallworld networks of infinite effective dimensionality [3,4,5,6]. These insights offer a new framework for understanding the strong finitesize effects and slow dynamics in systems undergoing such Anderson transitions, analogous to the manybody localization transition.
[1] Weitao Chen, Olivier Giraud, Jiangbin Gong, Gabriel Lemarié, arXiv:2312.17481, to be published in Phys. Rev. Res. (2024).
[2] Weitao Chen, Olivier Giraud, Jiangbin Gong, Gabriel Lemarié, arXiv:2405.10975, to be published in Phys. Rev. B (2024).
[3] I. GarcíaMata, O. Giraud, B. Georgeot, J. Martin, R. Dubertrand, and G. Lemarié, Phys. Rev. Lett. 118, 166801 (2017).
[4] I. GarcíaMata, J. Martin, R. Dubertrand, O. Giraud, B. Georgeot, and G. Lemarié, Phys. Rev. Research 2, 012020(R) (2020).
[5] I. GarcíaMata, J. Martin, O. Giraud, B. Georgeot, R. Dubertrand, and G. Lemarié, Phys. Rev. B 106, 214202 (2022).
[6] Weitao Chen et al., in preparation (2024).

15:05  15:30

Lev Vidmar
(Jožef Stefan Institute)
Similarity between a manybody quantum avalanche model and the ultrametric random matrix model
In the field of ergodicitybreaking phases, it has been recognized that quantum avalanches can destabilize manybody localization at a wide range of disorder strengths. This has in particular been demonstrated by the numerical study of a toy model, sometimes simply called the “avalanche model” or the “quantum sun model”, which consists of an ergodic seed coupled to a perfectly localized material. In this talk, we connect this toy model to a wellstudied model in random matrix theory, the ultrametric ensemble. We conjecture that the models share the following features. (1) The location of the critical point may be predicted sharply by analytics. (2) On the localized site, both models exhibit Fock space localization. (3) There is a manifold of critical points. On the critical manifold, the eigenvectors exhibit nontrivial multifractal behavior that can be tuned by moving on the manifold. (4) The spectral statistics at criticality is intermediate between Poisson statistics and random matrix statistics, also tunable on the critical manifold. We confirm numerically these properties.
J Šuntajs, L Vidmar, Physical Review Letters 129 (5), 060602 (2022)
J Šuntajs, M Hopjan, W De Roeck, L Vidmar, Physical Review Research 6 (2), 023030 (2024)

15:30  15:55

Fabian HeidrichMeisner
(Göttingen University)
Delocalization in a partially disordered interacting manybody system
We study a partially disordered onedimensional system with interacting particles. Concretely, we impose a disorder potential to only every other site, followed by a clean site. Our numerical analysis of eigenstate properties is based on the entanglement entropy and density distributions. Most importantly, at large disorder, there exist eigenstates with large entanglement entropies and significant correlations between the clean sites. These states have volumelaw scaling, embedded into a sea of arealaw states, reminiscent of inverted quantumscar states. These eigenstate features leave fingerprints in the nonequilibrium dynamics even in the largedisorder regime, with a strong initialstate dependence. We demonstrate that certain types of initial chargedensitywave states decay significantly, while others preserve their initial inhomogeneity, the latter being the typical behavior for manybody localized systems. This initialcondition dependent dynamics may give extra control over the delocalization dynamics at large disorder strength and should be experimentally feasible with ultracold atoms in optical lattices.

15:55  16:25

coffee break

16:25  17:00

Natalia Perkins
(University of Minnesota)
Dynamics of vacancyinduced modes in the nonAbelian Kitaev spin liquid

17:00  17:25

Sergey Syzranov
(University of California, Santa Cruz)
Quenched disorder and hidden energy scale in geometrically frustrated magnets (virtual)
Geometrically frustrated (GF) magnets are the main class of materials in which quantum spin liquids (QSLs) are sought. Quenched disorder, ubiquitous in all realistic materials, can lead to spin freezing and prevent the formation of the widely sought QSL states. As disorder can be introduced in a controlled way, it can also be used as a powerful tool for investigating the properties of GF materials. I will present a microscopic theory of spinglass freezing and magnetic susceptibility in GF magnets with quenched disorder. I will demonstrate that the properties of such materials are dominated by two distinct types of excitations, qualitatively similar to ringexchange and spinflip processes. I will show that the former are rather sensitive to quenched disorder and, for realistic amounts of disorder, lead to spinglassfreezing transitions at temperatures of the order of a small “hidden energy scale” determined by the properties of the clean GF medium.
Disorder also has a profound effect on the magnetic susceptibility of GF systems. Nonmagnetic atoms (vacancies) replacing magnetic ones are known to act as effective spins, “quasispins”. I will describe the values of quasispins in GF materials, the interactions between them and their interplay with the spin freezing.

18:00  19:00

dinner

19:00  22:00

poster session I
(focus on odd poster numbers)
