$N$-Body Efimov States from Two-Particle Noise

The ground state energies of universal $N$-body clusters tied to Efimov trimers, for $N$ even, are shown to be encapsulated in the statistical distribution of two particles interacting with a background auxiliary field at large Euclidean time when the interaction is tuned to the unitary point. Numerical evidence that this distribution is log normal is presented, allowing one to predict the ground state energies of the $N$-body system.

Figure 1

Histogram of the two-body correlator at large Euclidean time, $T$. Inset: Histogram of the logarithm of the correlator at the same value of $T$.

Figure 2

Deviation between the cumulant expansion [Eq. (9)] cut off at $N_{\kappa }$, and the converged value. The green circles represent the lattice data for the two-body correlator tuned to unitarity on a ${16}^3\times 1000$ lattice, while the blue diamonds are from a mock distribution created to reproduce moments corresponding to the energies found in [14].

Figure 3

Ratio of energies $E_0^{(N)}/E_0^{(4)}$ predicted by the LN distribution (green, lower points), compared to numerical calculations, (blue, upper points) [14], and (red, $N=6$, middle point) [15]. Inset: Numerical results for $E_6/E_4$ (from left to right) [13] (black), [14] (blue), and [15] (red).