Physicists map hidden order in quantum chaos, unlocking new computing models
Researchers have decoded how disordered quantum systems transition between chaotic and ordered states—a finding that could reshape how engineers design quantum computers and materials. The work reveals previously hidden patterns in quantum behavior, offering a roadmap for controlling quantum systems at scale.
Originaltitel: Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
We explore interpretations of the power-law banded random matrix (PLBRM) ensemble as Hamiltonians of one-dimensional quantum many-body systems. We introduce and compare a number of labeling schemes for assigning random matrix basis indices to many-body basis vectors. We compare the physical properties of the resulting Hamiltonians, focusing on the half-system eigenstate bipartite entanglement entropy. We show and quantify how the different PLBRM phases (ergodic, weakly ergodic, localized), known from the single-particle interpretation, can be interpreted as entanglement transitions in the quantum many-body interpretation. For the weakly ergodic phase, where spectral edge and bulk eigenstates show distinct behavior, we perform a detailed scaling analysis to provide a quantitative picture of the boundaries between different types of entanglement scaling behaviors. In particular, we identify and characterize an intermediate set of eigenstates whose entanglement entropy have volume law scaling but nonvanishing deviation from the Page value expected for maximally ergodic states.