无序系统与神经网络

We study the topology and localization properties of a generalized Su-Schrieffer-Heeger (SSH) model with a quasi-periodic modulated hopping. It is found that the interplay of off-diagonal quasi-periodic modulations can induce topological…

For over half a century, statistical mechanics of spin glasses played as a paradigm to model and interpret disparate phenomena, ranging from quantitative biology to computer science. However, despite the extensive body of research in this…

Quantum circuits have become a powerful tool in the study of many-body quantum physics, providing insights into both fast-thermalizing chaotic and non-thermalizing integrable many-body dynamics. In this work, we explore a distinct…

We propose a class of general non-Hermitian quasiperiodic lattice models with exponential hoppings and analytically determine the genuine complex mobility edges by solving its dual counterpart exactly utilizing Avila's global theory. Our…

The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to…

This article delves into the Hopfield neural network model, drawing inspiration from biological neural systems. The exploration begins with an overview of the model's foundations, incorporating insights from mechanical statistics to deepen…

We study stability of localisation under periodic driving in many-body Stark systems. We find that localisation is stable except near special resonant frequencies, where resonances cause delocalisation. We provide approximate analytical…

We consider the additive version of the matrix denoising problem, where a random symmetric matrix $S$ of size $n$ has to be inferred from the observation of $Y=S+Z$, with $Z$ an independent random matrix modeling a noise. For prior…

Extended and critical states are two common phenomena in Fibonacci quasicrystals. In this paper, we first reveal the difference between the extended phase and the critical phase in the extended-critical Fibonacci quasicrystal from the…

The statics of the Fredrickson-Andersen model (FAM) of the liquid-glass transition is solved on the Bethe lattice (BL). The kinetic constraints of the FAM imply on the BL an ergodicity-breaking transition to a (glassy) phase where a…

Large Language Models (LLMs) have demonstrated impressive performance. To understand their behaviors, we need to consider the fact that LLMs sometimes show qualitative changes. The natural world also presents such changes called phase…

Quasicrystals are fascinating and important because of their unconventional atomic arrangements, which challenge traditional notions of crystalline structures. Unlike regular crystals, they lack translational symmetry and generate unique…

Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…

Bismuth has been shown to be topological in its different allotropes and compounds, with one of the most notable examples being the Bi-Sb alloy, the first 3D topological insulator ever discovered. In this paper we explore two-dimensional…

Classification of quantum phases is one of the most important areas of research in condensed matter physics. In this work, we obtain the phase diagram of one-dimensional quasiperiodic models via unsupervised learning. Firstly, we choose two…

The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal…

Physics-based Ising machines (IM) have been developed as dedicated processors for solving hard combinatorial optimization problems with higher speed and better energy efficiency. Generally, such systems employ local search heuristics to…

Slow relaxation and glassiness have been the focus of extensive research attention, along with popular and technological interest, for many decades. While much understanding has been attained through mean-field and mode-coupling models,…

Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with…

Glass phases can be stabilized by quenched disorders, as in most spin-glass materials, or self-generated through kinetic freezing in disorder-free systems. A canonical example of the latter is structural glasses, which have been extensively…