Fluctuations, Quenched Disorder, and Strong Correlations

I will discuss that in all types of metallic magnets the coupling of the order parameter to the conduction electrons leads to an order-parameter susceptibility that is long-ranged at zero temperature, even in the non-magnetic phase. This is true for all known classes of ferromagnets, and also for antiferromagnets and spin-density wave systems, helimagnets, magnetic nematics, and altermagnets. The consequences for the magnetic quantum phase transition vary between different classes of magnets.

Walking from the old ferromagnetic forest towards the metallic land we encounter some Griffiths Isles. Thomas Vojta, our guide, points out the critical points and the conditions in disordered magnets. Can we see the relevant magnetic fluctuations in an alloy with quenched disorder? We present a small angle neutron scattering (SANS) study of a binary alloy close to the ferromagnetic (FM) quantum critical point (QCP). Ni-V with random atomic distribution shows indication of quenched disorder that modifies the magnetic quantum critical behavior. SANS data were collected on polycrystalline Ni-V samples with reduced FM ordering temperatures close to the QCP to resolve magnetic correlations. With the help of full polarized SANS analysis magnetic correlations at different length scales are revealed. Short-range fluctuations develop but long-range order still seems to persist in these weakly FM samples approaching the critical point. S. Bhattarai et al, Phys. Rev. B 107, 054409 (2023), (arXiv 2207.14196)

Recently, we showed that impurity levels in the starting constituent elements strongly affect superconductivity (Tc, delta C, and Tc(onset)) in UBe13 but not nearly so strongly in the conventional superconductor LuBe13. (J. S. Kim and G. R. Stewart, Physica B 635, 413792 (2022). Also, it has long been known - since the discovery of superconductivity in UPt3 (G.R. Stewart, Z. Fisk, J.O. Willis, and J.L. Smith, “Possibility of Coexistence of Bulk Superconductivity and Spin Fluctuations in UPt3,” Phys. Rev. Lett. 52, 679 (1984)) - that grinding *totally suppresses* superconductivity to below 0.05 K in the unconventional superconductor UPt3. In the current work we investigate the effect of defects introduced by various stages of grinding (down to a grain size between 20 and 45 microns and up to 125 micron grain size) on a number of unconventional superconductors, including ultra-high purity UBe13.

Whereas the amplitude of the zero-point motion of ions in strongly correlated electron systems is restricted to 1-2% of the equilibrium distances, the exponential sensitivity of the Kondo energy scale to these distances ensures, somewhat surprisingly, that at any moment in time there exists a broad distribution of Kondo energy scales, spanning orders of magnitude in temperature. Because of the vastly different time scales for ionic and electronic motion, to conduction electrons this dynamic distribution appears as a static one akin to chemical disorder, messing with the foundation of electronic theory, the periodic potential ansatz: V(r)=V(r+R). We discuss how the low-temperature response of quantum critical systems, both chemically doped and stoichiometric ones, can be readily understood as a manifestation of the underlying distribution of energy scales and how our current ‘organizing principles’ for the explanation of this behavior (such as the breakdown of quasiparticles at the quantum critical point) can be viewed as repair strategies for the usage of the periodic potential ansatz in the presence of substantial disorder.

In this talk I will consider the use of periodic measurements on driving transport and chirality in an otherwise undisturbed system

We present a controlled numerical study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in the one-dimensional Bose-Hubbard model at unit filling, providing evidence of the characteristic logarithmic finite-size scaling of the BKT transition.  Employing density matrix renormalization group and quantum Monte Carlo simulations under periodic boundary conditions, together with a systematic finite-size scaling analysis of bipartite particle number fluctuations, we resolve boundary-induced complications that previously obscured critical scaling. By leveraging a non-parametric Bayesian analysis, we determine the critical interaction strength with high precision, establishing a benchmark for BKT physics in one-dimensional quantum models.

Quenched disorder is generally considered inimical to the development of long-range ordered phases in condensed matter systems. In this talk, we show that this expectation is at times fallacious and infact disorder can lead to the emergence of new types of ordered phases. Focusing on the classical disordered J1-J2 XY model on the square lattice (with disorder modeled as vacancies), we demonstrate that in-line with standard lore, disorder fluctuations via an Imry-Ma type random field mechanism [1,2,3] lead to the melting of the (vestigial) collinear state that is known to exist in the translationally invariant avatar of this model. However, an order-by-disorder mechanism, predicated on disorder fluctuations, leads to the stabilization of an anticollinear vestigial phase at low temperatures [4,5]. We further show that the random field mechanism is rendered inoperative by building anticorrelations in the disorder distribution, thus stabilizing both collinear and anticollinear phases. These results, which are obtained by large-scale classical Monte-Carlo simulations, also very strikingly show that between these two vestigial phases elucidated above, there exists a narrow but robust intermediate emergent canted phase, characterized by a continuously varying relative angle between sublattice magnetizations. This phase is obtained due to competing effects of thermal and vacancy-induced order-by-disorder selections. Our numerical results are backed by an effective field theory description that brings out this competition between the aforementioned order-by-disorder mechanisms. [1] Y. Imry and S-k Ma., Phys. Rev. Lett. 35, 1399 (1975). [2] M. M. J. Miranda, I. C. Almeida, E. C. Andrade, and J. A. Hoyos, Phys. Rev. B 104,054201 (2021). [3] S. S. Kunwar, A. Sen, T. Vojta, and R. Narayanan, Phys. Rev. B 98, 024206 (2018). [4] C. L. Henley, Phys.Rev.Lett. 62, 2056 (1989). [5] D. Loison and P. Simon, Phys. Rev. B 61, 6114 (2000).

This talk will discuss experiments that reveal different types of far-from-equilibrium dynamics in strongly disordered two-dimensional electron systems depending on the range of the Coulomb interaction. The focus will be on protocols that demonstrate some key differences between glassy and many-body localization dynamics.

Hilbert space fragmentation, as it is currently investigated, primarily originates from specific kinematic constraints or emergent conservation laws in many-body systems with translation invariance. It leads to non-ergodic dynamics and possible breakdown of the eigenstate thermalization hypothesis. Also the relaxation dynamics of disordered systems, such as the XXZ model with random on-site fields, exhibits a slowing down that is naturally understood as a fragmentation in Fock-space. Specifically, the Fock-space decomposes into subspaces, potential-energy shells, which contain the accessible phase space for the relaxation of a quenched initial state. We propose that the slowing down of the relaxation dynamics reported in traditional MBL studies reflects a fragmentation of the potential energy shell, which - similar to a percolation transition - takes place if the disorder exceeds a threshold $W_\text{c}$. The connection of this phenomenon to many-body localization proper needs to be discussed.

Wigner crystals are extremely fragile, which is shown to result from very strong geometric frustration germane to long-range Coulomb interactions. Physically, this is manifested by a very small characteristic energy scale for shear density fluctuations, which are gapless excitations in a translationally invariant system. The presence of disorder, however, breaks translational invariance, thus suppressing gapless excitations and pushing them to higher density. We illustrate this general principle by explicit microscopic model calculations, showing that this mechanism very effectively stabilizes disordered Wigner lattices to much higher temperatures and densities than in the clean limit. On the other hand, we argue that in two dimensions disorder significantly ``smears" the melting transition, producing spatial coexistence of solid-like and liquid-like regions -- just as recently observed in STM experiments. Our results paint a new physical picture for melting of Wigner-Mott solids in two dimensions, corresponding to a Mott-Hubbard model with spatially varying local electronic bandwidth.

We investigate quench dynamics in the quantum $S=1/2$ XXZ antiferromagnetic chain with staggered and anisotropic interactions in the flat-band limit. Our quench protocol interchanges the odd- and even-bond strengths of a fully dimerized chain, enabling us to derive exact time-dependent states for arbitrary even system sizes by working in the Bell basis. We obtain closed-form, size-independent expressions for the von Neumann and second-order R\'enyi entanglement entropies. We further calculate exact Loschmidt echoes and the corresponding return rate functions across various anisotropies and system sizes, and identify Loschmidt zeros in finite chains. Our analysis reveals distinct finite-size scaling of the Loschmidt echo at critical times with chain length and identifies the precise conditions on the anisotropy parameter governing the periodicity of the dynamical observables. In addition to the analytic study, we perform two types of numerical experiments on IBM-Q quantum devices. First, we use the Hadamard test to estimate the Bell-basis expansion coefficients and reconstruct the dynamical states, achieving accurate entanglement entropies and the Loschmidt echo for small systems. Second, we implement Trotter-error-free time-evolution circuits combined with randomized Pauli measurements. Post-processing via statistical correlations and classical shadows yields reliable estimates of the second-order R\'enyi entanglement entropy and the Loschmidt echo, showing satisfactory agreement with exact results.

Deviations from the standard laws of Brownian motion, the linear time dependence of the mean squared displacement and the Gaussian probability density function, are quite commonly observed in an abundance of systems [1]. The physical mechanisms for these anomalies are non-universal, prompting the need for different stochastic models along with their identification from measured time series of dynamic motion. The model classification and parameter regression of anomalous diffusion can be successfully achieved by machine-learning tools such as Bayesian Deep Learning [2], which will be introduced along with a brief summary of the two recent AnDi (Anomalous Diffusion) Challenges [3,4]. The talk will focus on long-range dependent stochastic motion, identified in a large range of systems [5]. In particular, it will be discussed how to generalise such models to situations, in which the observed probability density is non-Gaussian, or when the processes display scaling exponents varying in time or space. Diffusion models with stochastically [6,7] and deterministically [8] varying diffusion coefficients and scaling exponents will be introduced. Applications to experimental data will be discussed. References: [1] E. Barkai, Y. Garini, and R. Metzler, Strange kinetics of single molecules in Living Cells, Phys. Today 65(8), 29 (2012); D. Krapf and R. Metzler, Strange interfacial molecular dynamics, Phys. Today 72(9), 48 (2019). [2] H. Seckler and R. Metzler, Bayesian deep learning for error estimation in the analysis of anomalous diffusion, Nature Commun. 13, 6717 (2022). [3] G. Munoz-Gil Objective comparison of methods to decode anomalous diffusion, Nature Commun. 12, 6253 (2021) [4] G. Munoz-Gilet al, Quantitative evaluation of methods to analyze motion changes in single-particle experiments, Nature Commun. 16, 6749 (2025). [5] O. Vilk, E. Aghion, T. Avgar, C. Beta, O. Nagel, A. Sabri, R. Sarfati, D. K. Schwartz, M. Weiss, D. Krapf, R. Nathan, R. Metzler, and M. Assaf, Unravelling the origins of anomalous diffusion: from molecules to migrating storks, Phys. Rev. Res. 4, 033055 (2022). [6] M. Balcerek, S. Thapa, K. Burnecki, H. Kantz, R. Metzler, A. Wylmanska, and A. Chechkin, Multifractional Brownian motion with telegraphic, stochastically varying exponent, Phys. Rev. Lett. 134, 197101 (2025). [7] W. Wang, F. Seno, I. M. Sokolov, A. V. Chechkin, and R. Metzler, Unexpected crossovers in correlated random-diffusivity processes, New J. Phys. 22, 083041 (2020). [8] W. Wang, M. Balcerek, K. Burnecki, A. V. Chechkin, S. Janusonis, J Slezak, T. Vojta, A. Wylmanska, and R. Metzler, Memory-multi-fractional Brownian motion with continuous correlations, Phys. Rev. Res. 5, L032025 (2023).

Gastrulation, the early stage of embryonic development, is an essential, highly conserved process in the development of all vertebrate embryos, including humans. During gastrulation, the embryo transforms from a single layer of epithelial cells into a three-layered structure of three major embryonic cell types, the ectoderm, the mesoderm and the endoderm, in a process involving large-scale cell and tissue movements. When not executed properly, it causes abortion of development and, in milder cases, leads to a wide range of congenital defects. The cellular mechanisms controlling gastrulation, when activated in the wrong place or at the wrong time, result in severe disease in adult life, such as cancer and malfunctioning of the immune system. Gastrulation requires the integration of critical cell behaviours, such as cell differentiation, division, and movement, through chemical and mechanical cell-cell signalling to achieve the morphogenesis essential for proper function. These interactions between signalling and cell behaviours create complex feedback loops between tissue, cell, and molecular length- and timescales that have evolved to enable the robust formation of complex multicellular structures. In this talk, using the vertex model for cell-level description of epithelial tissues, we will discuss how various forms of active processes, such as mechano-chemical feedback, cell growth, division, ingression, etc., couple to cell mechanics and lead to pattern formation and flows in model tissues. We will also make qualitative comparisons with primitive streak formation (i.e., gastrulation) in chick embryos.

Defects in strongly correlated systems are often viewed as unwanted perturbations. In quantum spin liquids, however, they can fundamentally reshape the emergent many-body state and reveal otherwise hidden aspects of fractionalization and gauge physics. In Kitaev quantum spin liquids, vacancies and magnetic impurities generate a remarkably rich spectrum of defect-induced phenomena, ranging from localized Majorana excitations and flux binding to impurity-controlled topological states. In this talk, I will discuss this defect-induced physics from two complementary perspectives. Vacancies reconstruct the local Majorana environment, producing low-energy resonances, enhanced local density of states, and characteristic tunneling signatures relevant to STM experiments. In time-reversal-symmetry-broken phases, they can bind Majorana zero modes and give rise to pronounced near-zero-bias features, while finite vacancy concentration and disorder reshape the low-energy continuum and thermodynamic response. I will then discuss spin-$3/2$ magnetic impurities as another route to flux physics: using an SO(6) Majorana representation and a self-consistent mean-field treatment, we show that flux-sector transitions are marked by discontinuous jumps in the impurity quadrupole moment, and that quadrupole correlations in a magnetic field decay with flux-sector-dependent rates. Together, these results establish defects as sensitive local probes of fractionalized excitations and emergent gauge structure in Kitaev magnets.

Magnetic frustration provides a fertile ground for the emergence of exotic states, including quantum spin liquids and topological textures. In real materials, however, disorder introduces a competing energy scale that can stabilize phases such as spin glasses or random singlets. In this talk, I discuss two examples of novel phases stabilized by disorder. First, I present a minimal model that captures the anomalous low-temperature thermodynamics of doped semiconductors, such as Si:P, across the metal-insulator transition. This model connects random-singlet formation on the insulating side to disordered Fermi-liquid behavior on the metallic side, highlighting the competition between Kondo screening and random-singlet formation as a central ingredient in understanding the low-temperature behavior of strongly disordered interacting systems. Second, I examine the effects of disorder on an extended Kitaev model. The additional terms in the model preserve its mapping to non-interacting Majorana fermions while selecting distinct flux backgrounds. We show that disorder stabilizes inhomogeneous flux configurations, significantly affecting the stability of the quantum spin liquid phase and its experimental signatures in thermodynamics and thermal transport.

I will discuss a newly proposed phase - "smectic vortex glass (SmVG), that arises when a mag-netic field is applied transversely to correlated columnar disorder. SmVG is characterized by an infinitely anisotropic electrical transport, resistive (dissipationless) for current perpendicular to (along) columnar defects. Its positional order is also quite unusual, long-ranged with true Bragg peaks along columnar defects and logarithmically rough vortex lattice distortions with quasi-Bragg peaks transverse to columnar defects. For low temperatures and sufficiently weak colum-nar-only disorder, SmVG is a true topologically-ordered “Bragg glass”, characterized by a van-ishing dislocation density. At sufficiently long scales the residual ever-present point disorder converts this state to a more standard, but highly anisotropic vortex glass.

Fluctuations are often regarded as noise; in fractional quantum Hall systems they can become a direct probe of topology. Strong correlations create quasiparticles with fractional charge and anyonic exchange statistics. I will discuss how these statistics can be accessed not by spatial exchange experiments, but through current cross-correlations. In mesoscopic anyon colliders, dilute quasiparticle beams collide at a quantum point contact, producing a universal signal governed by the exchange phase and edge scaling exponent. This signal can be viewed as braiding in the time domain. I will also discuss why finite pulse shapes matter in hierarchical states such as ν = 2/5, and outline HBT and antidot geometries aimed at extracting the bare exchange phase in realistic devices.

Performing a bibliometric analysis of the publications and the received citations I discuss the scientific correlations of Thomas Vojta. Particular emphasis is laid on his time at Chemnitz University. I then concentrate on quasicrystals which are unusual materials, because they possess long-range order but no translational symmetry. A simple one-dimensional example is the Fibonacci chain. Different methods are presented to construct such quasi-periodic systems like the Penrose tiling in two dimensions. Although quasicrystals are usually composed of metallic elements, they show very low electric conductivity which decreases with temperature and decreases also with the structural perfection of the quasicrystal. This observation can be related to the electronic states. In quasicrystals, there are no extended Bloch waves due to the aperiodicity. There exists a competition between the aperiodicity, which tends to localize the electron, and the repetitivity of the structure (the same structural motives appearing over and over again), which tends to have a delocalizing effect because electrons can tunnel between identical local environments. The result is that in simple model Hamiltonians one usually observes electronic states that are neither extended over the entire system nor exponentially localized, but so-called “critical” states that show a multifractal probability distribution. The particular physical properties of quasi-crystalline materials are discussed. Numerical simulations of the electronic states are presented. Finally topical technological applications are explained. Examples in art and architecture are also shown.