Browsing by Author "Peralta, Juan E."

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Determining the N-Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling
    (American Chemical Society, 2024) Massaccesi, Gustavo E.; Oña, Ofelia B.; Capuzzi, Pablo; Melo, Juan I.; Lain, Luis; Torre, Alicia; Peralta, Juan E.; Alcoba, Diego R.; Scuseria, Gustavo E.
    The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.
  • Thumbnail Image
    Item
    Magnetization Dynamics from Time-Dependent Noncollinear Spin Density Functional Theory Calculations
    (American Chemical Society, 2015) Peralta, Juan E.; Hod, Oded; Scuseria, Gustavo E.
    A computational scheme, based on a time-dependent extension of noncollinear spin density functional theory, for the simultaneous simulation of charge and magnetization dynamics in molecular systems is presented. We employ a second-order Magnus propagator combined with an efficient predictor-corrector scheme that allows us to treat large molecular systems over long simulation periods. The method is benchmarked against the low-frequency dynamics of the H–He–H molecule where the magnetization dynamics can be modeled by the simple classical magnetization precession of a Heisenberg–Dirac-van Vleck Hamiltonian. Furthermore, the magnetic exchange couplings of the bimetallic complex [Cu(bpy)(H2O)(NO3)2(μ-C2O4)] (BISDOW) are extracted from its low-frequency spin precession dynamics showing good agreement with the coupling obtained from ground state energy differences. Our approach opens the possibility to perform real-time simulation of spin-related phenomena using time-dependent density functional theory in realistic molecular systems.