# Quantum entanglement and the finite gap integration

**报告题目：**Quantum entanglement and the finite gap integration

**报告人：**Alexander Its 教授

**主持人：**陈勇 教授

**时间：**2014年7月23日 9:00

**地点：**中山北路数学馆201

**报告摘要：**

We calculate the Von Neumann and Renyi entropies of a large block of consecutive spins in the ground state of the XY spin chain on an infinite lattice. We also evaluate the spectrum of the corresponding reduced density matrix. The key feature of our approach is the use of Riemann-Hilbert and algebrageometric techniques of the theory of integrable systems for the asymptotic analysis of the Toeplitz determinants with matrix symbols.

**报告人简介：**

Alexander Its, the professor of Indiana University-Purdue University Indianapolis in American. He is a famous mathematician in the world. He has got the The prize of the Moscow Mathematical Society in 1976, the prize of the Leningrad Mathematical Society in 1981, the Hardy Fellow of the London Mathematical Society in 2002, and the Batsheva de Rothschild Fellow of Israel Academy of Sciences and Humanities in 2009. Prof. Its' major area is integrable systems. His current research interests are concentrated in the following directions: (a) Asymptotic analysis of the matrix models and orthogonal polynomials via Riemann-Hilbert and isomonodromy methods; (b) The asymptotic analysis of the correlation functions of quantum exactly solvable models and the related aspects of the theory of Fredholm and Toeplitz operators; (c) The theory of integrable nonlinear partial and ordinary differential equations of the KdV and Painleve types. In the area of random matrices, Its' main results for the last seven years have been obtained in collaboration with Pavel Bleher, as described above.