Joint ICTP/SISSA Statistical Physics Seminar, 29 July at 11:00am, by M.A. Rajabpour

[CMSP Seminars Secretariat]

---------------------------------------
Joint ICTP/SISSA Statistical Physics Seminar
---------------------------------------

** * * Tuesday 29 July**2025, 11:00**am ***(CET)** * **
*Luigi Stasi Seminar Room **(Leonardo Building)***
**
/Zoom: 
https://zoom.us/meeting/register/Zie5ON0VQmGkxhKl_NCSvw/<https://zoom.us/meeting/register/tJIsfuuhqjsrE9EZY2loNxNobg8Lf39NUVHJ>

Speaker:*Mohammad Ali Rajabpour *(Universidade Federal Fluminense, Brazil)

Title: *The Pfaffian Playbook: A Unified Toolkit for Gaussian Fermions 
in Any Basis**
*

Abstract:
Fermionic Gaussian states appear naturally as ground states and 
time-evolved states of exactly solvable models, such as the 
transverse-field Ising chain and the XY model, and serve as remarkably 
good variational approximations for interacting systems with weak to 
moderate correlations. Their efficient representation and manipulation 
is thus central to the study of quantum many-body physics. In this talk, 
I will present recent advances that lead to a fully explicit and 
efficient Pfaffian formula for amplitudes of fermionic Gaussian pure 
states in arbitrary local Pauli bases, along with a generalization to 
matrix elements of Gaussian operators, encompassing mixed states and 
dynamical observables. The construction relies on novel pfaffian 
relations and a Lie-algebraic framework generated by sign-encoding 
matrices spanning an algebra isomorphic to SO(2L). These tools provide 
both computational speed-ups and conceptual insights into the symmetry, 
duality, and structure of fermionic systems. Applications include 
formation probabilities, geometric entanglement, Shannon–Rényi 
entropies, post-measurement entanglement, dynamical phase transitions, 
optimized quantum tomography, and basis-rotated quench simulations.