Browsing by Author "Dukelsky, Jorge"

Now showing 1 - 3 of 3
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    Density matrix embedding from broken symmetry lattice mean fields
    (American Physical Society, 2014) Bulik, Ireneusz W.; Scuseria, Gustavo E.; Dukelsky, Jorge
    Several variants of the recently proposed density matrix embedding theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] are formulated and tested. We show that spin symmetry breaking of the lattice mean-field allows precise control of the lattice and fragment filling while providing very good agreement between predicted properties and exact results. We present a rigorous proof that at convergence this method is guaranteed to preserve lattice and fragment filling. Differences arising from fitting the fragment one-particle density matrix alone versus fitting fragment plus bath are scrutinized. We argue that it is important to restrict the density matrix fitting to solely the fragment. Furthermore, in the proposed broken symmetry formalism, it is possible to substantially simplify the embedding procedure without sacrificing its accuracy by resorting to density instead of density matrix fitting. This simplified density embedding theory (DET) greatly improves the convergence properties of the algorithm.
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    Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian
    (American Physical Society, 2016) Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo; Dukelsky, Jorge; Scuseria, Gustavo E.
    We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wave function. In between, we interpolate using a single parameter. The effective Hamiltonian is non-Hermitian and this polynomial similarity transformation theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero. Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit, whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction strengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.
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    Quasiparticle coupled cluster theory for pairing interactions
    (American Physical Society, 2014) Henderson, Thomas M.; Scuseria, Gustavo E.; Dukelsky, Jorge; Signoracci, Angelo; Duguet, Thomas
    We present an extension of the pair coupled cluster doubles (p-CCD) method to quasiparticles and apply it to the attractive pairing Hamiltonian. Near the transition point where number symmetry gets spontaneously broken, the proposed BCS-based p-CCD method yields significantly better energies than existing methods when compared to exact results obtained via solution of the Richardson equations. The quasiparticle p-CCD method has a low computational cost of O(N3) as a function of system size. This together with the high quality of results here demonstrated, points to considerable promise for the accurate description of strongly correlated systems with more realistic pairing interactions.