Complexity of quantum impurity problems

Understand

We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models.

• Such models describe a bath of free fermions coupled to a small interacting subsystem called an impurity.
• The full system consists of $n$ fermionic modes and has a Hamiltonian $H=H_0+H_{imp}$, where $H_0$ is quadratic in creation-annihilation operators and $H_{imp}$ is an arbitrary Hamiltonian acting on a subset of $O(1)$ modes.
• We show that the ground energy of $H$ can be approximated with an additive error $2^{-b}$ in time $n^3 \exp{[O(b^3)]}$.