Bootstrapping Symmetries in Quantum Many-Body Systems from the Cross Spectral Form Factor

arXiv:2604.01296 · quant-ph, cond-mat.stat-mech, cond-mat.str-el, hep-th · Submitted 2026-04-01 · Read on arXiv

quant-ph, cond-mat.stat-mech, cond-mat.str-el, hep-th

Submitted: 2026-04-01

Updated: 2026-09-19

Code: https://github.com/ZihanZhou26/xSFF_data

Terminology

• Hubbard Model — 24× in this paper · explained in 3 episodes
• Benchmark — 12× in this paper · explained in 2 episodes
• Consistency — 12× in this paper · explained in 3 episodes
• Hilbert Space — 11× in this paper · explained in 2 episodes
• Trace — 10× in this paper · explained in 2 episodes
• Effective Hamiltonian — 9× in this paper · explained in 2 episodes
• Degeneracy — 6× in this paper · explained in 3 episodes
• Generalization — 6× in this paper · explained in 13 episodes
• Entanglement — 5× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Random Matrix Theory — 2× in this paper
• Verification — 2× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Anyons — 1× in this paper · explained in 2 episodes
• Domain Walls — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Random Matrix Theory (RMT) — 1× in this paper · explained in 3 episodes
• Spectral Form Factor (SFF) — 1× in this paper · explained in 2 episodes

Sources

• Hilbert Space Fragmentation and Commutant Algebras
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Exhaustive Characterization of Quantum Many-Body Scars using Commutant Algebras
• From Symmetries to Commutant Algebras in Standard Hamiltonians
• Numerical Methods for Detecting Symmetries and Commutant Algebras
• Symmetries as Ground States of Local Superoperators: Hydrodynamic Implications
• Bridging Commutant and Polynomial Methods for Hilbert Space Fragmentation
• Numerical evidence for the non-Abelian eigenstate thermalization hypothesis
• Probing Hilbert space fragmentation and the block inverse participation ratio
• Spectral Decimation of Quantum Many-Body Hamiltonians
• Bounds in 4D Conformal Field Theories with Global Symmetry
• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Coarse-grained Bootstrap of Quantum Many-body Systems
• Bootstrapping Quantum Hamiltonians with Symmetry
• Fusion rules from entanglement
• Entanglement bootstrap approach for gapped domain walls
• Tensor categories: A selective guided tour
• From categories to anyons: a travelogue
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Non-perturbative Overlaps in JT Gravity: From Spectral Form Factor to Generating Functions of Complexity

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