相关论文: Logarithmic light cone, slow entanglement growth, …

We study entanglement properties of systems with spontaneously broken continuous symmetry. We find that in addition to the expected area law behavior, the entanglement entropy contains a subleading contribution which diverges…

A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…

Disorder-free localization (DFL) is a phenomenon as striking as it appears to be simple: a translationally invariant state evolving under a disorder-free Hamiltonian failing to thermalize. It is predicted to occur in a number of quantum…

We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other…

Large Language Models (LLMs), trained on massive corpora with billions of parameters, show unprecedented performance in various fields. Though surprised by their excellent performances, researchers also noticed some special behaviors of…

We study a one-dimensional system of spinless electrons in the presence of a long-range Coulomb interaction (LRCI) and a random chemical potential at each site. We first present a Tomonaga-Luttinger liquid (TLL) description of the system.…

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have recently achieved impressive results on reasoning benchmarks. Yet, growing evidence shows that these models often generate longer but ineffective chains of thought…

Ground states of local Hamiltonians are known to obey the entanglement entropy area law. While area law violation of a mild kind (logarithmic) is commonly encountered, strong area-law violation (more than logarithmic) is rare. In this…

Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…

Large Language Models (LLMs) often experience performance degradation during long-running interactions due to increasing context length, memory saturation, and computational overhead. This paper presents an adaptive context compression…

Long-range interactions allow far-distance quantum correlations to build up very fast. Nevertheless, numerical simulations demonstrated a dramatic slowdown of entanglement entropy growth after a sudden quench. In this work, we unveil the…

An open challenge in recent machine learning is about how to improve the reasoning capability of large language models (LLMs) in a black-box setting, i.e., without access to detailed information such as output token probabilities. Existing…

Text embeddings from PLM-based models enable a wide range of applications, yet their performance often degrades on longer texts. In this paper, we introduce a phenomenon we call Length Collapse, where embeddings of longer texts tend to…

We consider the relativistic Vlasov-Maxwell system in three dimensions and study the limiting asymptotic behavior as $t \to \infty$ of solutions launched by small, compactly supported initial data. In particular, we prove that such…

Thermalization and scrambling are the subject of much recent study from the perspective of many-body quantum systems with locally bounded Hilbert spaces (`spin chains'), quantum field theory and holography. We tackle this problem in 1D…

The parameter counts of the most widely used large language models (LLMs) are often withheld by their developers, leaving model size -- a primary reference point for interpreting capabilities and costs -- largely undisclosed. We propose a…

Reasoning Large Language Models (LLMs) enable test-time scaling, with dataset-level accuracy improving as the token budget increases, motivating adaptive reasoning -- spending tokens when they improve reliability and stopping early when…

The fixed-point logic LREC= was developed by Grohe et al. (CSL 2011) in the quest for a logic to capture all problems decidable in logarithmic space. It extends FO+C, first-order logic with counting, by an operator that formalises a limited…

The \textit{local learning coefficient} (LLC) is a principled way of quantifying model complexity, originally derived in the context of Bayesian statistics using singular learning theory (SLT). Several methods are known for numerically…

Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing…