Fragmented Many-body States of Spin-2 Bose Gas

TL;DR

This paper explores the complex fragmented ground states of a spin-2 Bose gas, revealing that exact states differ significantly from mean-field approximations and depend on particle number, with implications for understanding many-body quantum states.

Contribution

The study constructs exact ground states for spin-2 Bose gases and compares them with mean-field approximations, highlighting their limitations and the role of particle number in state fidelity.

Findings

Exact ground states differ from angular-averaged mean-field states.

Angular-averaged polar states fail for N ≥ 6.

Angular-averaged cyclic states only work for N divisible by 3.

Abstract

We investigate the fragmented many-body ground states of a spin-2 Bose gas in zero magnetic field.\ We point out that the exact ground state is not simply an average over rotationally-invariant mean-field states, in contrast to the spin-1 case with even number of particles N.\ We construct the exact ground states and compare them with the angular-averaged polar and cyclic states.\ The angular-averaged polar states fail to retrieve the exact eigenstate at $N$ $\ge$ $6$ while angular-averaged cyclic states sustain only for N with a multiple of $3$.\ We calculate the density matrices and two-particle density matrices to show how deviant the angular-averaged state is from the exact one.