Mohammad Ali Rajabpour
(Universidade Federal Fluminense, Brazil)

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.
 

Link to Zoom registration:
https://zoom.us/meeting/register/Zie5ON0VQmGkxhKl_NCSvw