Related papers: Graph-Theoretic Detection of Hilbert Space Fragmen…
Graph signal processing (GSP) leverages the inherent signal structure within graphs to extract high-dimensional data without relying on translation invariance. It has emerged as a crucial tool across multiple fields, including learning and…
In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two non-trivial subclasses,…
Analyzing the geometry of correlation sets constrained by general causal structures is of paramount importance for foundational and quantum technology research. Addressing this task is generally challenging, prompting the development of…
Certain wave functions of non-interacting quantum chaotic systems can exhibit "scars" in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories.…
Achieving fine-grained and structurally sound controllability is a cornerstone of advanced visual generation. Existing part-based frameworks treat user-provided parts as an unordered set and therefore ignore their intrinsic spatial and…
Quantum many-body scar is a recently discovered phenomenon weakly violating eigenstate thermalization hypothesis, and it has been extensively studied across various models. However, experimental realizations are mainly based on constrained…
Quantum entanglement in multipartite systems cannot be shared freely. In order to illuminate basic rules of entanglement sharing between qubits we introduce a concept of an entangled structure (graph) such that each qubit of a multipartite…
Exceptional points (EPs), indicative of parity-time (PT) symmetry breaking, play a central role in non-Hermitian physics, yet most studies begin from deliberately engineered effective Hamiltonians whose parameters are tuned to exhibit…
The past decade has seen a flourishing of advances in harmonic analysis of graphs. They lie at the crossroads of graph theory and such analytical tools as graph Laplacians, Markov processes and associated boundaries, analysis of path-space,…
We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes…
A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality.…
Theoretical research into many-body quantum systems has mostly focused on regular structures which have a small, simple unit cell and where a vanishingly small number of pairs of the constituents directly interact. Motivated by advances in…
Hilbert space fragmentation is an intriguing paradigm of ergodicity breaking in interacting quantum many-body systems with applications to quantum information technology, but it is usually adversely compromised in the presence of…
We investigate the quantum dynamics of the 1D spinless Fermi-Hubbard model with a linear-tilted potential. Surprisingly in a strong resonance regime, we show that the model can be described by the kinetically constrained effective…
Quantum many-body scarring (QMBS) -- a recently discovered form of weak ergodicity breaking in strongly-interacting quantum systems -- presents opportunities for mitigating thermalization-induced decoherence in quantum information…
Ergodicity breaking in isolated systems has emerged as an important frontier in the study of quantum many-body physics. While generic Hamiltonians are expected to obey the eigenstate thermalization hypothesis (ETH), recent studies on…
We develop a systematic theory of spectral decimation for quantum many-body Hamiltonians and show that it provides a quantitative probe of emergent symmetries in statistically mixed spectra. Building on an analytical description of…
Purpose: Accurate identification of hepatocystic anatomy is critical to preventing surgical complications during laparoscopic cholecystectomy. Deep learning models often struggle with occlusions, long-range dependencies, and capturing the…
This work establishes rigorous mathematical foundations connecting spectral graph theory, algebraic geometry, and string theory. We construct a canonical mapping whereby any finite graph \(G\) defines a compact Riemann surface \(X_{G}\)…
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…