Recorded 29 March 2023. Reinhold Schneider of the Technische Universität Berlin presents "A Multi-Reference Coupled Cluster Method for the Computation of Excited States and Tensor Networks (QC-DMRG)" at IPAM's Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing workshop. Abstract: Single reference Coupled Cluster calculation had become standard for computing highly accurate solutions of the electronic Schr odinger equation. State specic multi-reference CC in combination with DMRG provides a well proved tool to compute strong correlation eects. We aim to compute also degenerate and nearly degenerate states as well by a multi-state version of the bivariational principle, suitable for derivation of approximate multi-state (state-universal) coupled cluster meth- ods. There the idea is that for a Hamiltonian with n quasi-degenerate ground states, i.e. the n lowest eigenstates, we seek the projection P onto this set of eigenstates, that is P = Xn i=1 j nih ~ nj : (1) Indeed, we will dene our oblique projector P via a generalization of the bivariational principle which goes as follows: Consider the function S(P) = Trace(HP). Requiring S to be stationary upon arbitrary variations in the projector P (i.e., variations that preserve P2 = P and Trace(P) = n) leads to the two-sided Bloch equation (I ?? P)HP = 0; PH(I ?? P) = 0; (2) that is, the range of P (Py) is a right-invariant (left-invariant) subspace of H. The value of the functional at a critical point S = P i Ei, with n exact eigenvalues Ei, and He = PHP, an n n matrix, has Ei as its eigenvalues, while its eigenvectors determine the left and right eigenfunctions of H in the bases dened by P. In the spirit CC formulation we use the ansatz k := eTk jki with a reference k in a 1 CAS space , Tk consists of external excitations, together with the dual functions ~ k = h( ~k+k)je??Tk . Applying the bivariational formulation we derive a system of equations for these unknowns, which could be solved by a self consistent iteration. Moreover the nal method becomes extremely closed to state speci c CAS-CC and avoids the usual diculties like over parametrization of other state universal CC methods. The cost of the solution of the individual CC calculations in each iteration remains similar to that for standard single double coupled cluster calculations, like equation of motion (EOM). But it has to be incorporated into a self consistent iteration. The bottle neck of the present approach remains to be the full CI solutions on the CAS space. For this purpose we recommend recent highly ecient full CI solvers, e.g. by tensor approximation (DMRG) or Monte Carlo FCI. At the end we want to discuss related convergence analysis, mostly is based on earlier analysis of the Coupled Cluster approximation and on joint work with F. Faulstich (Berkeley), A. Laestadius (OlsoMet) and S. Kvaal (Dept. Chemistry U Oslo) Learn more online at: http://www.ipam.ucla.edu/programs/workshops/workshop-i-increasing-the-length-time-and-accuracy-of-materials-modeling-using-exascale-computing/