Variational wave functions for homogenous Bose systems

TL;DR

This paper investigates variational wave functions for the ground state of homogenous Bose systems, comparing different bases and their energy minimization, revealing how quasiparticle fluctuations affect the system's energy and spectrum.

Contribution

It introduces and analyzes new variational wave functions based on different orthonormal bases, including the Valatin-Butler basis and a shifted operators basis, to better understand ground state energies.

Findings

Lowest energy in VB basis involves large quasiparticle number with anomalous fluctuations.

Alternative basis yields smaller energy with normal fluctuations, approaching vacuum state.

Discussion on quasiparticle theories and spectral gap implications.

Abstract

We study variational wave functions of the product form, factorizing according to the wave vectors k, for the ground state of a system of bosons interacting via positive pair interactions with a positive Fourier transform. Our trial functions are members of different orthonormal bases in Fock space. Each basis contains a quasiparticle vacuum state and states with an arbitrary finite number of quasiparticles. One of the bases is that of Valatin and Butler (VB), introduced fifty years ago and parametrized by an infinite set of variables determining Bogoliubov's canonical transformation for each k. In another case, inspired by Nozi\`eres and Saint James the canonical transformation for k=0 is replaced by a shift in the creation/annihilation operators. For the VB basis we prove that the lowest energy is obtained in a state with ~sqrt{volume} quasiparticles in the zero mode. The number of k=0 physical particles is of the order of the volume and its fluctuation is anomalously large, resulting in an excess energy. The same fluctuation is normal in the second type of optimized bases, the minimum energy is smaller and is attained in a vacuum state. Associated quasiparticle theories and questions about the gap in their spectrum are also discussed.