Quantum Embedding with Lower Bounds - IPAM at UCLA

Explore quantum embedding theories in this 42-minute lecture presented by Michael Lindsey at IPAM's Multiscale Approaches in Quantum Mechanics Workshop. Delve into relaxations of the many-body ground state eigenvalue problem and discover tractable optimization approaches for solving these relaxations. Examine two distinct relaxation paradigms: one based on quantum marginals or reduced density operators, and another specific to fermions involving impurity problems similar to DMFT and DMET. Learn about the ground-state eigenvalue problem, algebras of operators, pairwise structure, semidefinite relaxation, and partial duality. Investigate the partial dual gradient ascent approach, AFH exact benchmarks, and the effect of global consistency constraints. Analyze the dependence of convergence on system size and explore related work in variational impurity-bath embedding. Gain insights into preliminary experiments and access references for further study in this comprehensive exploration of quantum embedding with lower bounds.

The ground state
The ground-state eigenvalue problem
Algebras of operators
Pairwise structure
Semidefinite relaxation
Partial duality
Partial dual gradient ascent approach
AFH exact benchmark
Effect of global consistency constraints
Dependence of convergence on system size
Related work
Variational impurity-bath embedding
Preliminary experiment
References and acknowledgments