Graph-energy centrality applied to Fock-space graphs captures weak ergodicity-breaking transitions in quantum many-body systems and scales to hundreds of sites or the thermodynamic limit.
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Numerical analysis shows that spectral statistics of a BPS-projected operator in an interpolating N=2 SYK model transition from random-matrix to Poisson behavior as the model moves from chaotic to integrable.
A flow equation for the resonance density exponent θ(w) derived in the SJA predicts resonance proliferation driving delocalization, with θ(w)>0 for localized phases and instability signaling thermalization, matching numerics in Anderson and MBL models.
Conductance fluctuations in 2D Anderson-disordered tight-binding systems transition from non-ergodic to ergodic with rising disorder while multifractality persists, driven by long-range correlations in weak disorder and distributional effects in strong disorder.
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Graph-theory measures capture weak ergodicity breaking on large quantum systems
Graph-energy centrality applied to Fock-space graphs captures weak ergodicity-breaking transitions in quantum many-body systems and scales to hundreds of sites or the thermodynamic limit.
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Chaos-Integrability Transition in the BPS Subspace of the $\mathcal{N}=2$ SYK Model
Numerical analysis shows that spectral statistics of a BPS-projected operator in an interpolating N=2 SYK model transition from random-matrix to Poisson behavior as the model moves from chaotic to integrable.
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Resonance Proliferation Across Localization Transitions
A flow equation for the resonance density exponent θ(w) derived in the SJA predicts resonance proliferation driving delocalization, with θ(w)>0 for localized phases and instability signaling thermalization, matching numerics in Anderson and MBL models.
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Multifractal and Ergodic Properties of Conductance Fluctuations under Strong Disorder
Conductance fluctuations in 2D Anderson-disordered tight-binding systems transition from non-ergodic to ergodic with rising disorder while multifractality persists, driven by long-range correlations in weak disorder and distributional effects in strong disorder.