Many-body wavefunctions for normal liquid $^3$He

TL;DR

This paper introduces advanced many-body wavefunctions with multi-body correlations for normal liquid helium-3, improving energy estimates and incorporating spin coupling, with implications for quantum simulations.

Contribution

It develops new trial wavefunctions with 3- and 4-body correlations and a stable method for evaluating pairing functions, enhancing modeling of liquid helium-3.

Findings

Wavefunctions lower energy and stabilize the ground state.

Inclusion of spin coupling improves Fermi liquid modeling.

Method for evaluating pairing functions is numerically stable.

Abstract

We present new trial wave-functions which include 3-body correlations into the backflow coordinates and a 4-body symmetric potential. We show that our wavefunctions lower the energy enough to stabilize the ground state energies of normal liquid $^3$He in the unpolarized state at all pressures in agreement with experiment; however, quantitative discrepancies remain. Further, we include strong spin coupling into the Fermi liquid by adapting pairing wave functions. We demonstrate a new, numerically stable method to evaluate pairing functions which is also useful for Path Integrals calculations at low, but non-zero temperatures.