Mixing Times Through Parent Hamiltonians in Fermionic Systems

Watch a 49-minute lecture from Duke University's Yu Tong at the Simons Institute exploring the analysis of mixing times in fermionic systems through parent Hamiltonians. Delve into the current methodology for constructing parent Hamiltonians in qubit Lindbladians, examining why direct application to fermionic systems fails to maintain fermionic locality. Learn how the third quantization formalism by Prosen resolves these issues, resulting in quasi-local fermionic parent Hamiltonians. Explore the implications for mixing times, particularly in fermionic systems with small but constant interaction terms per site. Conclude with an examination of open problems regarding quantum advantage and potential approaches for addressing strongly interacting fermionic systems.