Systems exhibiting Hilbert-space fragmentation are nonergodic, with their Hamiltonians decomposing into exponentially many blocks in the computational basis (e.g., the Ising basis). In many cases, these blocks can be labeled by the eigenvalues of statistically localized integrals of motion (SLIOMs), which play a role in fragmented systems analogous to that of local integrals of motion in integrable systems.
While a nonzero perturbation typically eliminates all nontrivial conserved quantities in integrable models, we demonstrate for the t–Jz chain that an appropriately chosen perturbation can gradually eliminate SLIOMs one by one, progressively merging the fragmented subspaces. This gradual recovery of ergodicity manifests as an extended critical regime characterized by multiple peaks in the fidelity susceptibility.
Furthermore, I will show how basic tools from spectral graph theory — such as the Fiedler vector and modularity — can be used to analyze fragmented and nearly fragmented systems.
In today’s revolutionary AI development, physics has played a significant role, as it is obvious from the Novel prize in 2024. In this talk, I point out a certain similarity between neural networks and quantum mechanics. Both have almost one century of history, while their intertwining started quite recently.
In the first half of the colloquium, I briefly summarize the reasons why neural networks are strong tools in physics, and introduce the basic AI methods. As a director of MLPhys initiative in Japan, I will report recent results of research unifying AI and theoretical physics in Japan, ranging from lattice QFT and condensed matter physics to automated mathematics.
In the second half of the colloquium, I explain our discovery of the similarity between neural networks and quantum mechanics. I provide a novel map with which a wide class of Euclidean quantum mechanical systems can be cast into the form of a neural network with a statistical summation over network parameters, which brings about a neural network representation of interacting quantum systems / field theories. In this manner, two major fields --- AI and physics --- can be joined together, which hopefully will foster the coming century of sciences.
Spicules are ubiquitous, small-scale plasma jets that populate the lower solar atmosphere. They are seen prominently in chromospheric observations and also exhibit signatures in the transition region and lower corona. More recently, these highly dynamic spicular jets in observations have been reported to be associated with upward propagating EUV intensity perturbations in the corona. A similar link has been found in previous simulations. This can have important implications for understanding mass and energy transport in the solar atmosphere. However, the physical origin and properties of these Propagating Coronal Disturbances (PCDs), and their spicular connection, are not yet fully understood. In this ongoing work, we explore the connection of PCDs with spicules by performing 2D radiative MHD simulations using the Pencil Code, where a forest of spicules is self-consistently produced in the solar atmosphere powered by the subsurface convective processes. By using the technique of Lagrangian tracking on the simulated snapshots, we find that the convection generates “acceleration fronts” by several mechanisms, including, for example, (1) squeezing by granular buffeting, (2) collapse of granules, and (3) solar global modes, aided by magnetic reconnection. These acceleration fronts are also regions of strong compression or shocks that propagate outward through the solar atmosphere at the speed of slow magneto-acoustic waves. The passage of shock fronts successively through any point in the atmosphere produces saw-toothed velocity signals. We analyze wavelet power spectra for these modeled velocity signals sampled at several atmospheric heights in the simulations, along with other diagnostics, and use them to investigate how the slow MHD shock waves may be the common driver behind both PCDs and spicules.
