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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Momentum distribution of boson and fermion systems in Jastrow theory

Stefano Fantoni

Published Mar 1, 1978• 94 citations
Publisher
DOI
10.1007/bf02813391

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We study many-body correlations in the ground state of a general quantum system of bosons or fermions by including an additional Jastrow function in our recently proposed variational coupled-cluster method. Our approach combines the advantages of state-dependent correlations in the coupled-cluster theory and of the strong, short-ranged correlations of the Jastrow function. We apply a generalized linked-cluster expansion for the Jastrow wave function and provide a detailed analysis for practical evaluation of the Hamiltonian expectation value as an energy functional of the Jastrow function and the bare density-distribution functions introduced and calculated in our earlier publications; a simple, first-order energy functional is derived and detailed formulas for the higher-order contributions are provided. Our energy functional does not suffer the divergence as most coupled-cluster calculations often do when applying to Hamiltonians with hardcore potentials. We also discuss possible applications of our technique, including applications to strongly correlated fermion systems.
An occupation-number formulation is considered for a many-particle boson system when the ground state is described by the Bijl-Dingle-Jastrow (BDJ) type of variational wave function. A nonunitary operator acting on the state function of a noninteracting boson system is introduced to convert the BDJ function in configuration space into an equivalent state function in second-quantized space. The momentum distribution function is derived in an infinite series in terms of the liquid-structure function and the correlation function. In the case of the optimum variational description under the uniform limit, the leading term of the obtained result is found to agree with the Bogoliubov formula evaluated in the weak-coupling limit. The same analysis in the occupation-number space also reproduces the mean kinetic energy calculated in configuration space.
The wave function of a Tonks-Girardeau (T-G) gas of strongly interacting bosons in one dimension maps onto the absolute value of the wave function of a noninteracting Fermi gas. Although this fermionization makes many aspects of the two gases identical, their equilibrium momentum distributions are quite different. We observed dynamical fermionization, where the momentum distribution of a T-G gas evolves from bosonic to fermionic after its axial confinement is removed. The asymptotic momentum distribution after expansion in one dimension is the distribution of rapidities, which are the conserved quantities associated with many-body integrable systems. Our measurements agree well with T-G gas theory. We also studied momentum evolution after the trap depth is suddenly changed to a new nonzero value, and we observed the theoretically predicted bosonic-fermionic oscillations.