Entanglement of free-fermion systems, signal processing and algebraic combinatorics
arXiv:2401.07150 · doi:10.1007/978-3-031-91266-5_23
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 -polynomial association schemes is seen to yield a simplifying framework.
arXiv comment11 pages; This paper is based on the presentation made by Luc Vinet at Gravity, Strings and Fields: A conference in honour of Gordon Semenoff organized by the CRM. v2: Minor modifications to match the published version
References in corpus (14)
- Perfect state transfer in quantum spin networks
- Calculation of reduced density matrices from correlation functions
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Properties of the entanglement Hamiltonian for finite free-fermion chains
- Free-fermion entanglement and spheroidal functions
- Free-Fermion entanglement and orthogonal polynomials
- Algebraic Heun operator and band-time limiting
- A graph with fractional revival
- Entanglement in Fermionic Chains and Bispectrality
- Entanglement of inhomogeneous free fermions on hyperplane lattices
- Entanglement of Free Fermions on Johnson Graphs
- Multipartite information of free fermions on Hamming graphs
- Entanglement of Free Fermions on Hadamard Graphs
- Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes