Inhomogeneous XX spin chains and quasi-exactly solvable models

Abstract

We establish a direct connection between inhomogeneous XX spin chains (or free fermion systems with nearest-neighbors hopping) and certain QES models on the line giving rise to a family of weakly orthogonal polynomials. We classify all such models and their associated XX chains, which include two families related to the Lamé (finite gap) quantum potential on the line. For one of these chains, we numerically compute the Rényi bipartite entanglement entropy at half filling and derive an asymptotic approximation thereof by studying the model's continuous limit, which turns out to describe a massless Dirac fermion on a suitably curved background. We show that the leading behavior of the entropy is that of a $c=1$ critical system, although there is a subleading $\log (\log N)$ correction (where $N$ is the number of sites) unusual in this type of models.

arXiv comment37 pages, 6 figures. Minor revision of previous version, two references added

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Cited by in corpus (9)

• Cosmic-Ray Positrons Strongly Constrain Leptophilic Dark Matter
• Entanglement of inhomogeneous free fermions on hyperplane lattices
• Entanglement entropy of inhomogeneous XX spin chains with algebraic interactions
• Entanglement in non-critical inhomogeneous quantum chains
• Absence of logarithmic enhancement in the entanglement scaling of free fermions on folded cubes
• Fermionic logarithmic negativity in the Krawtchouk chain
• Entanglement of Inhomogeneous Free Bosons and Orthogonal Polynomials
• Local fermion density in inhomogeneous free-fermion chains: a discrete WKB approach
• $su(2)$ symmetry of XX spin chains