P. Calabrese and J. L. Cardy, Entanglement entropy and quantum field theory: A Non-technical introduction, Int. J. Quant. Inf, vol.4, p.429, 2006.

P. Calabrese, J. Cardy, and B. Doyon, Entanglement entropy in extended quantum systems, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.50, p.500301, 2009.

H. Casini and M. Huerta, Entanglement entropy in free quantum field theory, J. Phys, vol.42, p.504007, 2009.

N. Laflorencie, Quantum entanglement in condensed matter systems, Phys. Rept, vol.646, pp.1-59, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01384552

J. I. Latorre and A. Riera, A short review on entanglement in quantum spin systems, Journal of Physics A Mathematical General, vol.42, issue.50, p.504002, 2009.

G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Entanglement in Quantum Critical Phenomena, Phys Rev Lett, vol.90, issue.22, p.227902, 2003.

I. Peschel, Letter to the Editor: Calculation of reduced density matrices from correlation functions, Journal of Physics A Mathematical General, vol.36, issue.14, pp.205-208, 2003.

I. Peschel and V. Eisler, Reduced density matrices and entanglement entropy in free lattice models, Journal of Physics A Mathematical General, vol.42, issue.50, p.504003, 2009.

D. Gioev and I. Klich, Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture, Phys Rev Lett, vol.96, issue.10, p.100503, 2006.

I. Peschel, On the reduced density matrix for a chain of free electrons, Journal of Statistical Mechanics: Theory and Experiment, issue.6, p.6004, 2004.

V. Eisler and I. Peschel, Free-fermion entanglement and spheroidal functions, Journal of Statistical Mechanics: Theory and Experiment, issue.4, p.4028, 2013.

V. Eisler and I. Peschel, Properties of the entanglement Hamiltonian for finite free-fermion chains, Journal of Statistical Mechanics: Theory and Experiment, issue.10, 2018.

D. Slepian, Some comments on Fourier analysis, uncertainty and modeling, SIAM Rev, vol.25, issue.3, pp.379-393, 1983.

H. J. Landau, An Overview of Time and Frequency Limiting, pp.201-220, 1985.

J. J. Duistermaat and F. A. Grünbaum, Differential equations in the spectral parameter, Communications in Mathematical Physics, vol.103, issue.2, pp.177-240, 1986.

R. Koekoek and R. F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Faculty of Information Technology and Systems, Department of Technical Mathematics and Informatics, 1998.

R. Koekoek, P. A. Lesky, and R. F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their q-Analogues, 2010.

F. A. Grünbaum, A new property of reproducing kernels for classical orthogonal polynomials, J. Math. Anal. Appl, vol.95, issue.2, pp.90123-90126, 1983.

M. Perlstadt, Chopped orthogonal polynomial expansionssome discrete cases, SIAM Journal on Algebraic Discrete Methods, vol.4, issue.1, pp.94-100, 1983.

M. Perlstadt, A property of orthogonal polynomial families with polynomial duals, SIAM Journal on Mathematical Analysis, vol.15, issue.5, pp.1043-1054, 1984.

F. A. Grünbaum, L. Vinet, and A. Zhedanov, Algebraic Heun Operator and Band-Time Limiting, Communications in Mathematical Physics, vol.364, issue.3, pp.1041-1068, 2018.

F. A. Grünbaum, L. Vinet, and A. Zhedanov, Tridiagonalization and the Heun equation, Journal of Mathematical Physics, vol.58, issue.3, p.31703, 2017.

G. Kristensson, Second Order Differential Equations: Special Functions and Their Classification, 2010.

A. Ronveaux, Heun's Differential Equations, 1995.

R. K. Perline, Discrete time-band limiting operators and commuting tridiagonal matrices, SIAM J. Algebraic Discrete Methods, vol.8, issue.2, pp.192-195, 1987.

F. Grünbaum, Eigenvectors of a toeplitz matrix: Discrete version of the prolate spheroidal wave functions, SIAM Journal on Algebraic Discrete Methods, vol.2, issue.2, pp.136-141, 1981.

J. Cardy and E. Tonni, Entanglement hamiltonians in two-dimensional conformal field theory, J. Stat. Mech, vol.1612, issue.12, p.123103, 2016.

G. Vitagliano, A. Riera, and J. I. Latorre, Volume-law scaling for the entanglement entropy in spin-1/2 chains, New Journal of Physics, vol.12, issue.11, p.113049, 2010.

E. Tonni, J. Rodríguez-laguna, and G. Sierra, Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems, Journal of Statistical Mechanics: Theory and Experiment, vol.4, p.43105, 2018.

P. Terwilliger, Two linear transformations each tridiagonal with respect to an eigenbasis of the other; an algebraic approach to the Askey scheme of orthogonal polynomials, 2004.

C. H. Lee, P. Ye, and X. Qi, Position-momentum duality in the entanglement spectrum of free fermions, J. Stat. Mech, issue.10, p.10023, 1410.

Z. Huang and D. P. Arovas, Entanglement spectrum and Wannier center flow of the Hofstadter problem, Physical Review B, vol.86, issue.24, 2012.

J. A. Carrasco, F. Finkel, A. González-lópez, and P. Tempesta, A duality principle for the multi-block entanglement entropy of free fermion systems, Scientific Reports, vol.7, p.11206, 2017.

K. Nomura and P. Terwilliger, Linear transformations that are tridiagonal with respect to both eigenbases of a Leonard pair, Linear Algebra Appl, vol.420, issue.1, pp.198-207, 2007.

,

J. C. Mason, D. C. Handscomb, and C. Polynomials, , 2002.

A. Zhedanov, Classical Sturmian sequences, 2019.

C. Albanese, M. Christandl, N. Datta, and A. Ekert, Mirror Inversion of Quantum States in Linear Registers, Phys Rev Lett, vol.93, issue.23, p.230502, 2004.

A. Kay, A Review of Perfect State Transfer and its Application as a Constructive Tool, Int. J. Quantum Inf, vol.8, p.641, 2010.

R. Chakrabarti, J. Van-der, and J. , Quantum communication through a spin chain with interaction determined by a Jacobi matrix, Journal of Physics A Mathematical General, vol.43, issue.8, p.85302, 2010.

L. Vinet and A. Zhedanov, How to construct spin chains with perfect state transfer, Physical Review A, vol.85, issue.1, p.12323, 2012.

F. Colomo and A. G. Pronko, Square ice, alternating sign matrices and classical orthogonal polynomials, J. Stat. Mech, vol.0501, p.1005, 2005.