Controllable-dimension fractal agglomerates in 3D exhibit a localization-non-ergodic transition with sub-extensive critical states at critical α, while 2D versions show only localized states.
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Derives asymptotic real-space decay of flat-band projectors: exponential with algebraic prefactor for linearly independent CLS, compact for orthogonal limit, and power-law for singular limit with diverging localization length.
In 1D all-bands-flat condensates, infinitesimal interactions trigger a geometry-driven transition to a nematic manifold for θ ≥ π/8, with density-modulated states at θ=π/4 thermally selected via order-by-disorder.
citing papers explorer
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Localization--non-ergodic transition in controllable-dimension fractal networks from diffusion-limited aggregation
Controllable-dimension fractal agglomerates in 3D exhibit a localization-non-ergodic transition with sub-extensive critical states at critical α, while 2D versions show only localized states.
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Real space decay of flat band projectors from compact localized states
Derives asymptotic real-space decay of flat-band projectors: exponential with algebraic prefactor for linearly independent CLS, compact for orthogonal limit, and power-law for singular limit with diverging localization length.
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Nematic Phase Transitions and Density Modulations in 1D Flat Band Condensates
In 1D all-bands-flat condensates, infinitesimal interactions trigger a geometry-driven transition to a nematic manifold for θ ≥ π/8, with density-modulated states at θ=π/4 thermally selected via order-by-disorder.