Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
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In the long-range Haldane-Shastry model, pristine Poisson level statistics emerge only with combined position disorder and random magnetic fields, with an approximate scaling collapse governed by the product αδ when SU(2) symmetry is broken.
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Long-range nonstabilizerness of topologically encoded states from mutual information
Mutual information between non-contractible regions on the torus fully classifies long-range nonstabilizerness for toric-code states but leaves a finite subset undetected in the doubled-Fibonacci string-net model.
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Level statistics of the disordered Haldane-Shastry model with $1/r^\alpha$ interaction
In the long-range Haldane-Shastry model, pristine Poisson level statistics emerge only with combined position disorder and random magnetic fields, with an approximate scaling collapse governed by the product αδ when SU(2) symmetry is broken.