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The Wiener-Hopf factorization of algebraic matrix valued functions with the help of the Riemann theta function. Quantum entanglement of the spin chains as a case study.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

The evaluation of the entropy  of entanglement of the ground state in a wide family of one-dimensional quantum spin can be reduced to the Wiener-Hopf factorization of certain 2×2 algebraic  matrix valued functions. We show how this factorization can be performed using the apparatus of the Riemann-Hilbert method  and algebra-geometricintegration  borrowed from the theory of integrable systems. We would like to thinkabout these calculations as a basis for a conjecture that  the Wiener-Hopf factorization of a general  algebraic matrix   can be  performed in terms of the Riemann theta functions associated with a certain  algebraic curve. The talk is based on the speaker works with  V. Korepin and B. Q. Jin and on his works with  F. Mezzadri and M. Y. Mo.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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