Quantum Impurity and Quantum Embedding Theory - IPAM at UCLA

Explore quantum impurity and quantum embedding theory in this 51-minute lecture presented by Lin Lin from the University of California, Berkeley. Delve into the quantum many-body problem, starting with non-interacting systems and progressing to quantum impurity problems. Examine various static quantum embedding theories, including a concise derivation of Density Matrix Embedding Theory (DMET). Learn about bath construction, basis rotation, interacting impurity Hamiltonians, and matching conditions. Investigate least squares and convex optimization approaches in DMET, and address challenges with gapless problems. Discover the basic structure of quantum impurity and the sparsity of self-energy. Explore dynamical quantum embedding theories, focusing on enhancing the robustness of Dynamical Mean-Field Theory (DMFT) using semidefinite relaxation. Gain insights into the Luttinger-Ward functional, Green's function domains, and Lindsey's conjecture.

Intro
Quantum many body problem
Simplest setting: non-interacting system
Next simplest setup: quantum impurity problem
Examples of (static) quantum embedding theory
A concise derivation of DMET: bath construction from non-interacting systems
Basis rotation
Interacting impurity Hamiltonian
Matching condition
Least squares (LS-DMET)
Reformulate the fitting problem
Convex optimization (CVX-DMET)
What to do with gapless problems?
Basic structure quantum impurity: sparsity of the self energy
Examples of dynamical quantum embedding theory
Enhancing the robustness of DMFT using semidefinite relaxation (SDA)
Luttinger Ward functional
Domain of Green's function
Lindsey's conjecture on the domain of LW functional
Conclusion