Entanglement of inhomogeneous free fermions on hyperplane lattices

Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes

“…The presence of oscillations in figure 3 can be attributed to sub-leading terms that have not been fully characterized in the present analysis. Similar oscillations have been observed in Krawtchouk chains and a conjecture regarding the sub-leading terms was proposed in [34].…”

“…This corresponds to a logarithmic violation of the area law in one dimension [6], which is typical for one-dimensional free-fermion models described by an underlying CFT with central charge c = 1. The scaling (62) thus suggests that the anti-Krawtchouk chain is described by a CFT in curved space [36] with c = 1, similarly to the Krawtchouk chain [32,34].…”

“…In the following, we investigate the scaling of S(j) as a function of j. The entanglement properties of inhomogeneous free-fermion chains solved by orthogonal polynomials have been intensely studied recently [30][31][32][33][34][35]. We fix the ratios κ := K/d and ξ := (d − L)/(j + 1) and use (53) to compute S(j) via exact numerical diagonalization of the chopped correlation matrix (51).…”

Bethe ansatz diagonalization of the Heun-Racah operator

“…It could also be instructive to find directly a presentation of the relations of these dynamical operators within a R-matrix formalism in order to find more complicated Heun operators. For example, Heun operators associated to multivariate polynomials has been introduced in [8] and it should prove interesting to study their spectra through the algebraic Bethe ansatz.…”

“…They also naturally lead to the commuting tridiagonal operator [27] arising in the computation of the entanglement entropy for 1D free Fermion models [23,24] with couplings given by the recurrence coefficients of orthogonal polynomials of the Askey scheme. This has been generalized to free fermions on vertices of distance regular graphs [21,10,11] or to multidimensional networks associated to the multivariate Krawtchouk polynomials [8].…”