Modified Szegö–Widom Asymptotics for Block Toeplitz Matrices with Zero Modes
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10955_2018_2177_ReferencePDF.pdf
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Author(s)
Basor, E.
Dubail, J.
Emig, T.
Santachiara, R.
Date Issued
October 17, 2018
Publisher
Springer US
Version
Author's final manuscript
Abstract
Abstract
The Szegö–Widom theorem provides an expression for the determinant of block Toeplitz matrices in the asymptotic limit of large matrix dimension n. We show that the presence of zero modes, i.e, eigenvalues that vanish as
$$\alpha ^n$$
α
n
,
$$|\alpha |<1$$
|
α
|
<
1
, when
$$n\rightarrow \infty $$
n
→
∞
, requires a modification of the Szegö–Widom theorem. A new asymptotic expression for the determinant of a certain class of block Toeplitz matrices with one pair of zero modes is derived. The result is inspired by one-dimensional topological superconductors, and the relation with the latter systems is discussed.
MIT Department
MultiScale Materials Science for Energy and Environment, Joint MIT-CNRS Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10955-018-2177-8
