A new many-particle variational method

Hiroshi Takizawa, Akihide Oguchi

Elmar Heeb

Jay D. Mancini, Vassilios Fessatidis, Samuel P. Bowen +1 more

Виктор Павлович Маслов

In solving the problem of finding a temperature distribution which, at zero temperature, corresponds to superfluidity, i.e., to nonzero energy, the author tried to quantize free energy. This was done on the basis of supersecondary quantization whose special case is the usual secondary quantization for bosons and with the help of which new representations of the Schrödinger equation were obtained. The supersecondary quantization allowed the author to construct a variational method whose zero approximation are the Hartree-Fock and Bogolyubov-BCSch variational principles. This method works especially well in the case of not a large number of particles. The new quantization and the variational method are of general character and can be used in the quantum field theory.

S. P. Merkur′ev

V. Ya. Krivnov, А. А. Овчинников

A new variational method for determining the ground-state energy of quasi-1D systems is proposed. The method consists of decomposition of a lattice into non-interacting blocks. A trial wavefunction is the product of exact ground-state block functions multiplied by operator correlation factors. The ground-state energy of a spin-1/2 and fermionic particle ladder is evaluated. The calculation is very simple and gives energies with an accuracy of about 2% or even less.