Analysis of The Coupled-Cluster Method Tailored by Tensor-Network States in Quantum Chemistry.

We analyze the tailored coupled-cluster (TCC) method, which is a multi-reference formalism that combines the single-reference coupled-cluster (CC) approach with a full configuration interaction (FCI) solution covering the static correlation. This covers in particular the high efficiency coupled-cluster method tailored by tensor-network states (TNS-TCC). For statically correlated systems, we introduce the conceptually new CAS-ext-gap assumption for multi-reference problems which replaces the unreasonable HOMO-LUMO gap. We characterize the TCC function and show local strong monotonicity and Lipschitz continuity such that Zarantonello's Theorem yields locally unique solutions fulfilling a quasi-optimal error bound for the TCC method. We perform an energy error analysis revealing the mathematical complexity of the TCC-method. Due to the basis-splitting nature of the TCC formalism, the error decomposes into several parts. Using the Aubin-Nitsche-duality method we derive a quadratic (Newton type) error bound valid for the linear-tensor-network TCC scheme DMRG-TCC and other TNS-TCC methods.