Semigroup influence matrices as quantum impurity solvers

We introduce a framework for describing the real-time dynamics of quantum

impurity models out of equilibrium which is based on the influence matrix

approach. By replacing the dynamical map of a large fermionic quantum

environment with an effective semi-group influence matrix (SGIM) which acts on

a reduced auxiliary space, we overcome the limitations of previous proposals,

achieving high accuracy at long evolution times. This SGIM corresponds to a

uniform matrix-product state representation of the influence matrix and can be

obtained by an efficient algorithm presented in this paper. We benchmark this

approach by computing the spectral function of the single impurity Anderson

model with high resolution. Further, the spectrum of the effective dynamical

map allows us to obtain relaxation rates of the impurity towards equilibrium

following a quantum quench. To demonstrate the applicability to dissipative

models, for a quantum impurity model with on-site two-fermion loss, we compute

the spectral function and confirm the emergence of Kondo physics at large loss

rates. Finally I will show how this real-time impurity solver can be applied to

study homogenously interacting models using dynamical mean field theory (DMFT)