Asymptotics of block Toeplitz determinants with piecewise continuous symbols

Basor, E., Ehrhardt, T. and Virtanen, J. (2024) Asymptotics of block Toeplitz determinants with piecewise continuous symbols. Communications on Pure and Applied Mathematics, 78 (1). pp. 120-160. ISSN 1097-0312 doi: 10.1002/cpa.22223

Abstract/Summary

We determine the asymptotics of the block Toeplitz determinants det Tn(φ) as n → ∞ for N × N matrix-valued piecewise continuous functions φ with a finitely many jumps under mild additional conditions. In particular, we prove that det Tn(φ) ∼ G nn ΩE as n → ∞, where G, E, and Ω are constants that depend on the matrix symbol φ and are described in our main results. Our approach is based on a new localization theorem for Toeplitz determinants, a new method of computing the Fredholm index of Toeplitz operators with piecewise continuous matrix-valued symbols, and other operator theoretic methods. As an application of our results, we consider piecewise continuous symbols that arise in the study of entanglement entropy in quantum spin chain models.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/117419
Identification Number/DOI	10.1002/cpa.22223
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Wiley
Download/View statistics	View download statistics for this item