Adaptive cluster approximation for reduced density-matrix functional theory

Abstract

A method, called the adaptive cluster approximation (ACA), for single-impurity Anderson models is proposed. It is based on reduced density-matrix functional theory, where the one-particle reduced density matrix is used as the basic variable. The adaptive cluster approximation introduces a unitary transformation of the bath states such that the effect of the bath is concentrated to a small cluster around the impurity. For this small effective system one can then either calculate the reduced density-matrix functional numerically exact from Levy's constrained-search formalism or approximate it by an implicit approximation of the reduced density-matrix functional. The method is evaluated for single-impurity Anderson models with finite baths. The method converges rapidly to the exact result with the size of the effective bath.

Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers

“…the full system. The following section shows how the ACA [16] can be used to create a smaller effective system for which the density-matrix functional has to be evaluated, thereby drastically reducing the qubit count.…”

“…The starting point of the ACA [16] is a density-matrix functional F Ŵlocal [ρ (1) ] with an interaction…”

“…This makes the approach very similar to the VQE in the sense that a parametrized trial state for the many-particle state is prepared on the quantum computer and the parameters of this state are modified with a minimization algorithm running on a classical computer till the measured total energy is minimal. While the approach proposed here introduces additional equality constraints on the minimum compared to the VQE, the formulation allows for novel approximations like the adaptive cluster approximation (ACA) [16].…”

Off-shell effective energy theory: A unified treatment of the Hubbard model from d=1 to d=∞

“…Furthermore, we note that the maps Υ K , Υ X directly provide a description of the physical space of all ( ∆n ρ, ∆ d ρ), yielding a concrete approximation that resolves the N-representability problem [37][38][39][40][41][42] in this class of Hamiltonians. Therefore, OET provides an alternative viewpoint to this problem, which is of strong interest in the field of quantum chemistry and solid state physics [43][44][45][46][47][48][49][50][51][52].…”

New methods for the ab-initio simulation of correlated systems

“…However, for example for NiO, the local approximation of the interaction gives only a small number of interacting one-particle states, but the one-particle reduced density matrix for a solid contains in principle an infinite number of one-particle states. By proposing the adaptive cluster approximation [Schade and Blöchl, 2018] in chapter 8, we show that in this situation the density-matrix functional can be well approximated with 24 or 36 spin-orbitals. We also show how the transformation of the one-particle basis constructed within the adaptive cluster approximation can be used to drastically reduce the computational cost of ground-state calculations and time evolutions of quantum dots or single-impurity Anderson models in the framework of matrix product states (MPS, [White, 1992Östlund and Rommer, 1995;Schollwöck, 2005;Schollwöck, 2011]).…”