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      Symmetry Constraints and Variational Principles in Diffusion Quantum Monte Carlo Calculations of Excited-State Energies

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          Abstract

          Fixed-node diffusion Monte Carlo (DMC) is a stochastic algorithm for finding the lowest energy many-fermion wave function with the same nodal surface as a chosen trial function. It has proved itself among the most accurate methods available for calculating many-electron ground states, and is one of the few approaches that can be applied to systems large enough to act as realistic models of solids. In attempts to use fixed-node DMC for excited-state calculations, it has often been assumed that the DMC energy must be greater than or equal to the energy of the lowest exact eigenfunction with the same symmetry as the trial function. We show that this assumption is not justified unless the trial function transforms according to a one-dimensional irreducible representation of the symmetry group of the Hamiltonian. If the trial function transforms according to a multi-dimensional irreducible representation, corresponding to a degenerate energy level, the DMC energy may lie below the energy of the lowest eigenstate of that symmetry. Weaker variational bounds may then be obtained by choosing trial functions transforming according to one-dimensional irreducible representations of subgroups of the full symmetry group.

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          Fermion nodes

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            New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field

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              MONTE CARLO METHODS IN AB INITIO QUANTUM CHEMISTRY

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                Author and article information

                Journal
                12 March 1999
                Article
                10.1103/PhysRevB.60.4558
                cond-mat/9903204
                56601bb4-6845-4e93-afbc-c1e8735a847f
                History
                Custom metadata
                CMTH99-WMCF1
                Phys. Rev. B 60, 4558-4570 (1999).
                14 pages, RevTeX with epsf, 5 eps figures, submitted to Phys. Rev. B
                cond-mat

                Condensed matter
                Condensed matter

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