Colored Weingarten Calculus for Block-Unitary Ensemble

arXiv:2609.30385 · quant-ph, cond-mat.stat-mech · Submitted 2026-09-24 · Read on arXiv

quant-ph, cond-mat.stat-mech

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Entanglement — 8× in this paper · explained in 3 episodes
• Hilbert Space — 8× in this paper · explained in 2 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Conservation Laws — 2× in this paper · explained in 3 episodes
• Eigenstate Thermalization Hypothesis — 2× in this paper
• Eigenstate Thermalization Hypothesis (ETH) — 2× in this paper · explained in 4 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Entanglement Entropy — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Eigenstate thermalization and rotational invariance in ergodic quantum systems
• Weingarten Calculus
• Free Independence and Unitary Design from Random Matrix Product Unitaries
• Typical entanglement entropy with charge conservation
• Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
• Universal Spreading of Nonstabilizerness and Quantum Transport
• Coherence dynamics in quantum many-body systems with conservation laws
• Non-Gaussianity of random quantum states
• Classical shadows of fermions with particle number symmetry
• Generalized Free Cumulants for Quantum Chaotic Systems
• Eigenstate Thermalization Hypothesis with projective representation
• Eigenstate chaos in the presence of non-Abelian symmetries
• A random purification channel for arbitrary symmetries with applications to fermions and bosons
• Theory of the Matchgate Commutant
• The commutant of fermionic Gaussian unitaries

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