Five-Body Efimov Effect and Universal Pentamer in Fermionic Mixtures

Abstract

We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non- Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind

Energy of N two-dimensional bosons with zero-range interactions

“…Single-particle moves of this type are similar to the ones we dealt with in the fermionic case [16]. Here we have to calculate the normalization integral and sample a product of two two-dimensional Laplacians,…”

“…Our method can be generalized to include the leading-order effective-range correction to the N-body energy (as has been done in three-dimensions [16]). One can then estimate the energy correction due to finite-range effects associated with the finite width of the cloud in the quasi-two-dimensional case.…”

“…The solution procedure is then based on a stochastic process (diffusion of walkers) in the 2M-dimensional space {q 1 , K, q M } for which equation (8) is the detailed-balance condition and F is (proportional to) the probability density distribution. We now briefly describe the procedure in the bosonic case (for more technical details applicable in general see [16] and its supplemental material).…”

“…In this paper we derive a many-body integral equation to describe the system directly in the zero-range limit and solve it by using our recently developed stochastic algorithm [16]. We tabulate B N for all N26 and claim the values c 1 =−2.06(4) and c 2 =−8(2) for the first terms in the large-N expansion…”

Efimov Physics Beyond Three Particles

“…Adding another fermion, the relevant symmetry is 0 − , therefore F (q 1 , q 2 , q 3 ) = f (q 1 , q 2 , q 3 ,q 1 ·q 2 ,q 1 ·q 3 ,q 2 ·q 3 )q 1 ·q 2 ×q 3 , but the resulting six-dimensional integral equation is too hard to be solved with conventional method. Hence a novel method, which we call the STM-DMC method, is introduced [27,32], where f is treated as density probability function for so called walkers, whose stochastic dynamics is governs in such a way that the detailed-balance condition is Eq. 6.…”