On interacting fermions and bosons with definite total momentum

Abstract

Any {\it exact} eigenstate with a definite momentum of a many-body Hamiltonian can be written as an integral over a {\it symmetry-broken} function $\Phi$. For two particles, we solve the problem {\it exactly} for all energy levels and any inter-particle interaction. Especially for the ground-state, $\Phi$ is given by the simple Hartree-Fock/Hartree ansatz for fermions/bosons. Implications for several and many particles as well as a numerical example are provided.

References in corpus (4)

• Theory of Bose-Einstein condensation in trapped gases
• Stationary solutions of the one-dimensional nonlinear Schroedinger equation: II. Case of attractive nonlinearity
• Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions
• Continuous configuration-interaction for condensates in a ring

Cited by in corpus (5)

• Fragmentation of Bose-Einstein Condensates
• Exact ground state of finite Bose-Einstein condensates on a ring
• Critical fluctuations in a soliton formation of attractive Bose-Einstein condensates
• The generator coordinate method in time-dependent density-functional theory: memory made simple
• Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation