Fundamental groups of non-compact arithmetic hyperbolic n-manifolds (n≥4) contain thin surface subgroups; doubles of cusped ones embed as GFERF subgroups of SO^+(n+1,1).
Uniform Expansion Bounds for Cayley Graphs of SL_2 (F_p ) , urldate =
2 Pith papers cite this work. Polarity classification is still indexing.
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Many r-local Hamiltonians, including Pauli strings, random high-rank operators, and high-rank operators, admit sparsifications with o(n^r) terms that (1±ε)-approximate the original Hamiltonian on all states.
citing papers explorer
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Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$
Fundamental groups of non-compact arithmetic hyperbolic n-manifolds (n≥4) contain thin surface subgroups; doubles of cusped ones embed as GFERF subgroups of SO^+(n+1,1).
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Many Hamiltonians Are Sparsifiable
Many r-local Hamiltonians, including Pauli strings, random high-rank operators, and high-rank operators, admit sparsifications with o(n^r) terms that (1±ε)-approximate the original Hamiltonian on all states.