Exactness of wave functions from two-body exponential transformations in many-body quantum theory

Journal Article · Thu Jan 01 04:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.012507· OSTI ID:20640602

Mazziotti, David A ^[1]

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1. Department of Chemistry and the James Franck Institute, University of Chicago, Chicago, Illinois 60637 (United States)

Recent studies have considered the possibility that the exact ground-state wavefunction from any Hamiltonian with two-particle interactions may be generated from a single finite two-body exponential transformation acting on an arbitrary Slater determinant [Piecuch et al., Phys. Rev. Lett. 90, 113001 (2003)]. Using the Campbell-Baker-Hausdorff relation, we show that it is difficult for the variational minimum of this trial wave function to satisfy the contracted Schroedinger equation which is a necessary and sufficient condition for the wave function to satisfy the Schroedinger equation. A counterexample is presented through the Lipkin quasispin model with 4-50 fermions. When the number of fermions exceeds four, the wave function from a finite two-body exponential transformation is shown to be inexact. If the trial wave function ansatz is extended to include products of finite two-body exponential transformations acting on an arbitrary Slater-determinant reference, then we show that the ansatz includes the exact ground-state wave function from any Hamiltonian with only two-particle interactions. Connections between the two-body exponential transformation of the wave function and recent research on two-body exponential similarity transformations of the Hamiltonian [S.R. White, J. Chem. Phys. 117, 7472 (2002)] are discussed.

• OSTI ID: 20640602
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 1 Vol. 69; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
FERMIONS
GROUND STATES
HAMILTONIANS
PARTICLE INTERACTIONS
SCHROEDINGER EQUATION
SLATER METHOD
TRANSFORMATIONS
TWO-BODY PROBLEM
VARIATIONAL METHODS
WAVE FUNCTIONS