Inhomogeneous XX spin chains and quasi-exactly solvable models

Finkel, Federico; González-López, Artemio

doi:10.1088/1742-5468/abb237

Inhomogeneous XX spin chains and quasi-exactly solvable models

Federico Finkel
(
- Madrid U.
)
,
Artemio González-López
(
- Madrid U.
)

Jul 1, 2020

41 pages

Published in:

J.Stat.Mech. 2009 (2020) 093105

Published: Sep 23, 2020

e-Print:

2007.00369 [cond-mat.str-el]

DOI:

10.1088/1742-5468/abb237 (publication)

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Abstract: (IOP)

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 continuum 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.

Note:

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

solvable lattice models
spin chains
ladders and planes
entanglement in extended quantum systems
conformal field theory

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