Entanglement in Fermionic Chains and Bispectrality

Abstract

Entanglement in finite and semi-infinite free Fermionic chains is studied. A parallel is drawn with the analysis of time and band limiting in signal processing. It is shown that a tridiagonal matrix commuting with the entanglement Hamiltonian can be found using the algebraic Heun operator construct in instances when there is an underlying bispectral problem. Cases corresponding to the Lie algebras $\mathfrak{su}(2)$ and $\mathfrak{su}(1,1)$ as well as to the q-deformed algebra ${\mathfrak{so}}_q(3)$ at $q$ a root of unity are presented.

21 pages; invited contribution to the Roman Jackiw 80th Birthday Festschrift (World Scientific, 2020); v2: minor changes

References in corpus (2)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Position momentum Duality in the Entanglement Spectrum of Free Fermions

Cited by in corpus (12)

• Entanglement Hamiltonians: from field theory, to lattice models and experiments
• Entanglement of inhomogeneous free fermions on hyperplane lattices
• Local and non-local properties of the entanglement Hamiltonian for two disjoint intervals
• On the Bisognano-Wichmann entanglement Hamiltonian of nonrelativistic fermions
• Fermionic logarithmic negativity in the Krawtchouk chain
• Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
• The rational Sklyanin algebra and the Wilson and para-Racah polynomials
• Bethe ansatz diagonalization of the Heun-Racah operator
• A new commutativity property of exceptional orthogonal polynomials
• Time and band limiting operator and Bethe ansatz
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Entanglement of free-fermion systems, signal processing and algebraic combinatorics