报告题目：Shannon-Rényi Entropy in Many-Body Systems: Theory, Numerics, Experiments, and a Hint of Berezin-Grassmann Magic

报告人：M. A. Rajabpour 教授（Federal University of Fluminense, Brazil）

报告时间：2025年6月23日（周一）下午15:30 - 16:30

报告地点：北洋园校区49教410室

报告摘要：

The Shannon-Rényi entropy, derived from formation probabilities in many-body wavefunctions, has emerged as a powerful probe of complexity, universality, and phase transitions in quantum systems. In this talk, I present a unified framework for understanding and computing the Shannon-Rényi entropy across a variety of spin chains, combining analytical insight, numerical techniques, and experimental realizations. Special focus is given to free fermionic systems, such as the transverse-field Ising chain, where the Rényi entropy can be exactly mapped to the sum of powers of principal minors (SPPM) of certain correlation matrices. To address the computational challenges posed by SPPM—an #P-hard problem for integer powers greater than one—I introduce a novel representation based on Berezin-Grassmann integrals. This approach unveils hidden symmetries and enables a tractable mean-field approximation, yielding accurate predictions for Rényi entropies and critical behavior in free fermion models. Notably, I also discuss recent experimental breakthroughs where, for the first time, the central charge of critical quantum chains such as the transverse-field Ising and XXZ models was extracted on quantum hardware using Shannon-Rényi entropy. This demonstrates that information-theoretic quantities—once considered primarily theoretical—can now be directly measured in real quantum devices. This work shows how a seemingly abstract matrix function, when paired with field-theoretic techniques, opens a pathway to both analytical understanding and experimental access to universal observables in quantum many-body systems—with a hint of Berezin-Grassmann magic.

报告人简介：

He received their PhD in 2007 from Sharif University of Technology. After completing postdoctoral positions at the University of Torino and SISSA in Italy, he moved to Brazil at the end of 2012. Since 2014, he has been a professor at Universidade Federal Fluminense (UFF). For the first ten years of their research career, they primarily worked on stochastic Loewner evolution (SLE) and conformal field theories (CFT). However, since 2012, his focus has shifted to many-body quantum systems. His research explores these systems' equilibrium and non-equilibrium properties using a combination of analytical, numerical, and field-theoretical methods.