Quantum versus mean-field collapse in a many-body system

Abstract

The recent analysis, based on the mean-field approximation (MFA), has predicted that the critical quantum collapse of the bosonic wave function, pulled to the center by the inverse-square potential in the three-dimensional space, is suppressed by the repulsive cubic nonlinearity in the bosonic gas, the collapsing ground state being replaced by a regular one. We demonstrate that a similar stabilization acts in a quantum many-body system, beyond the MFA. While the collapse remains possible, repulsive two-particle interactions give rise to a metastable gaseous state, which is separated by a potential barrier from the collapsing regime. The stability of this state improves with the increase of the number of particles. The results are produced by calculations of the variational energy, with the help of the Monte Carlo method.

10 pages, 4 figures

References in corpus (7)

• Multipartite Entanglement Signature of Quantum Phase Transitions
• Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition
• Quantum and Topological Criticalities of Lifshitz Transition in Two-Dimensional Correlated Electron Systems
• Superfluid Fermi-Fermi mixture: phase diagram, stability, and soliton formation
• Mixing-demixing in a trapped degenerate fermion-fermion mixture
• One- and two-dimensional reductions of the mean-field description of degenerate Fermi gases
• Off-diagonal Ground State Properties of a 1D Gas of Fermi Hard Rods

Cited by in corpus (10)

• Suppression of the quasi-two-dimensional quantum collapse in the attraction field by the Lee-Huang-Yang effect
• From Efimov Physics to the Bose Polaron using Gaussian States
• Dissociation of one-dimensional matter-wave breathers due to quantum many-body effects
• Singular mean-field states: A brief review of recent results
• Spontaneous symmetry breaking of self-trapped and leaky modes in quasi-double-well potentials
• Double-layer Bose-Einstein condensates: A quantum phase transition in the transverse direction, and reduction to two dimensions
• Fall of a Particle to the Center of a Singular Potential: Classical vs. Quantum Exact Solutions
• Self-stabilized Bose polarons
• A new form of liquid matter: quantum droplets
• The inverse-square interaction phase diagram: unitarity in the bosonic ground state