Affiliation:
1. American Institute of Mathematics Pasadena California USA
2. University of California Santa Cruz California USA
3. University of Reading Reading UK
4. University of Helsinki Helsinki Finland
Abstract
AbstractWe determine the asymptotics of the block Toeplitz determinants as for matrix‐valued piecewise continuous functions with a finitely many jumps under mild additional conditions. In particular, we prove that
where , , and are constants that depend on the matrix symbol 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.
Funder
Engineering and Physical Sciences Research Council
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