The one-dimensional Holstein model and Holstein-Hubbard model have no nontrivial local conserved quantities other than the Hamiltonian and total fermion number.
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Rank deficiency of local Hamiltonians in classically fragmented models generates entangled frozen states, splitting mobile sectors into quantum Krylov subspaces and frozen entangled parts, with weak and strong quantum fragmentation distinguished by the number and ergodicity of irreducible blocks.
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.
In finite 2D disordered systems, Anderson localization at low energies coexists with quantum scarring at higher energies due to energy-dependent localization lengths and finite-size effects, producing observable signatures in intensity patterns and spectral statistics.
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Proof of the absence of local conserved quantities in the Holstein model
The one-dimensional Holstein model and Holstein-Hubbard model have no nontrivial local conserved quantities other than the Hamiltonian and total fermion number.
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Quantum Hilbert Space Fragmentation and Entangled Frozen States
Rank deficiency of local Hamiltonians in classically fragmented models generates entangled frozen states, splitting mobile sectors into quantum Krylov subspaces and frozen entangled parts, with weak and strong quantum fragmentation distinguished by the number and ergodicity of irreducible blocks.
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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.
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Coexistence of Anderson Localization and Quantum Scarring in Two Dimensions
In finite 2D disordered systems, Anderson localization at low energies coexists with quantum scarring at higher energies due to energy-dependent localization lengths and finite-size effects, producing observable signatures in intensity patterns and spectral statistics.