Projected coupled cluster theory

Abstract

Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wave functions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.

Attenuated coupled cluster: a heuristic polynomial similarity transformation incorporating spin symmetry projection into traditional coupled cluster theory

“…While we would like to try to combine SUHF and CC, it is difficult to see how to do so in a straightforward manner because SUHF variationally solves for the energy as an expectation value, and CC solves for the energy and wavefunction projectively. Besides our own efforts, [11][12][13] there have also been other attempts to combine SUHF with residual correlation methods. [40][41][42] In this work, we take a new approach, exploiting our recent formulation of SUHF for singlet states as a polynomial similarity transformation of particle-hole excitations out of a symmetry-adapted reference determinant.…”

“…Although SUHF is traditionally written variationally, we have recently formulated SUHF for singlet states (s = 0) as a polynomial similarity transformation (PoST) of particle-hole excitations out of a symmetry-adapted reference determinant in the mathematical language of traditional coupled cluster. [11,13] In this work, we present attenuated coupled cluster (attCC), in which we use the PoST formulation of SUHF to inform a modificaton of the CCD amplitude equations that protects the method from breakdown in the presence of strong correlation.…”

Extending spin‐symmetry projected coupled‐cluster to large model spaces using an iterative null‐space projection technique

“…Spin‐projection on broken‐symmetry CC, which we call spin‐extended CC (ECC), is therefore an attractive candidate for describing both static and dynamical correlation effects (we have to clarify that it is different from the extended coupled‐cluster of Arponen, which was derived from the bivariational principle in 1983) and many authors have explored its potential . However, challenges remain in combining CC and spin‐projection, with two particular difficulties.…”

“…First, introducing into CC prevents the resultant equations from naturally terminating. Recently, Scuseria et al introduced the disentangled cluster, based on which the nonterminating energy expression is elegantly approximated . For the present study, we use a truncated scheme based on the Taylor expansion of the cluster operator, named spin‐extended approximate CC (EACC) .…”

Efficient formulation of full configuration interaction quantum Monte Carlo in a spin eigenbasis via the graphical unitary group approach

“…orbitals (i, j, k, l) weighted with |V ijkl | -identify type of generatorê ij,kl (RR, LL or RL)Create one random nonzero spin-conserving excitation |m → |m by looping over orbitals in the excitation range via the branching tree: -choose possible branches with prob. ∝ | m |Ê ij |m | or | m |ê ij,kl |m | -calculate coupling coefficients on-the-fly according to Eqs (30). or(45)Method:-spin-conserving excitation |m → |m with gen. prob.…”