Beyond Order: Unveiling Hidden Quantum Structure
![The Aubry-André model exhibits a complex phase diagram characterized by hyperuniformity classes, revealing scaling behaviors of [latex]SQS_Q[/latex] that depend on both the parameter λ and the Fermi level’s position relative to the band edges-with scaling exponents of 1, 0.618, and 2 for Fermi levels crossing bands at λ = 1, 2, and 3, respectively-and a nuanced landscape of the scaling exponent ν that diversifies significantly at λ = 2, all within a system size of N = 17711.](https://arxiv.org/html/2601.18331v1/Fig1_newnew.png)
A new framework leveraging quantum hyperuniformity reveals previously obscured phases and transitions in quantum systems by characterizing the suppression of long-range fluctuations.
![The Aubry-André model exhibits a complex phase diagram characterized by hyperuniformity classes, revealing scaling behaviors of [latex]SQS_Q[/latex] that depend on both the parameter λ and the Fermi level’s position relative to the band edges-with scaling exponents of 1, 0.618, and 2 for Fermi levels crossing bands at λ = 1, 2, and 3, respectively-and a nuanced landscape of the scaling exponent ν that diversifies significantly at λ = 2, all within a system size of N = 17711.](https://arxiv.org/html/2601.18331v1/Fig1_newnew.png)
A new framework leveraging quantum hyperuniformity reveals previously obscured phases and transitions in quantum systems by characterizing the suppression of long-range fluctuations.

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![The study reveals that the imaginary component of pseudo-entropy [latex]Sp^{I}_{pA} [/latex] exhibits opposing behaviors contingent upon the sign of the anisotropy parameter [latex]\Delta_{y} [/latex], demonstrated through variations in [latex]\beta|\Delta| [/latex] at [latex]\beta = 10 [/latex] with [latex]\delta_{x} [/latex] and [latex]\delta_{y} [/latex] set to specific values, suggesting a fundamental sensitivity within the system to directional asymmetry.](https://arxiv.org/html/2601.17810v1/x2.png)
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![Lepton number violating (LNV) operators effectively suppress the primordial baryon asymmetry, as demonstrated by constraints derived from [latex]B^{+}\to K^{+}\nu\nu decay[/latex] and [latex]0\nu\beta\beta decay[/latex], with regions corresponding to [latex]\eta\_{B}=6.14\times 10^{-{10}}[/latex] delineating the extent of this suppression-particularly evident in scenarios where neutrino masses are primarily explained by dimension-7 LNV operators.](https://arxiv.org/html/2601.16422v1/x4.png)
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![The study of conformal towers within the Ashkin-Teller model, under [latex]A - h^z[/latex] boundary conditions at [latex]\lambda = 0.2[/latex] and [latex]\lambda = 0.7071[/latex], reveals level crossings at [latex]h^z = \pm \lambda[/latex]-points corresponding to [latex]d\theta[/latex]-as evidenced by finite-size DMRG data extrapolated to the thermodynamic limit, suggesting a critical sensitivity to boundary conditions within the system.](https://arxiv.org/html/2601.16951v1/x14.png)
New research explores the fascinating boundary behavior of a quantum system, revealing a complex landscape of phases and transitions.