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Entanglement of free-fermion systems, signal processing and algebraic combinatorics
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abstract
This paper offers a review of recent studies on the entanglement of free-fermion systems on graphs that take advantage of methods pertaining to signal processing and algebraic combinatorics. On the one hand, a parallel with time and band limiting problems is used to obtain a tridiagonal matrix commuting with the chopped correlation matrix in bispectral situations and on the other, the irreducible decomposition of the Terwilliger algebra arising in the context of $P$-polynomial association schemes is seen to yield a simplifying framework.
Forward citations
Cited by 3 Pith papers
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Hidden symmetry at the diabolical points of a biaxial spin
At every diabolical point of a biaxial spin, two noncommuting spectral-cut projectors commute with the Hamiltonian; their rank gives the exact multiplicity, and a negative determinant gives Chern charge −1 to every lo...
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Entanglement Hamiltonian after a local quench
For a local joining quench, the entanglement Hamiltonian of a finite free-fermion chain is local in the continuum limit, with distinct left/right-moving inverse temperatures, matching exact numerics.
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Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
For inhomogeneous free-boson chains, the leading entanglement entropy is (a*/6) log N, where a* is the scaling exponent of the region where the local potential vanishes.
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