Abstract
Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic ^4{text {He}} exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic ^3{text {He}} is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid ^3{text {He}} without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor S({mathbf {q}}), the momentum distribution n({mathbf {q}}), and the static density response function chi ({mathbf {q}}). In addition, the dynamic structure factor S({mathbf {q}},omega ) is rigorously reconstructed from imaginary-time PIMC data. From simulations of ^3{text {He}}, we derived the familiar phonon–maxon–roton dispersion function that is well-known for ^4{text {He}} and has been reported previously for two-dimensional ^3{text {He}} films (Nature 483:576–579 (2012)). The comparison of our new results for both S({mathbf {q}}) and S({mathbf {q}},omega ) with neutron scattering measurements reveals an excellent agreement between theory and experiment.
Highlights
path integral Monte Carlo (PIMC) results have been derived by introducing the uncontrolled fixed-node approximation
An accurate description of physical effects such as the lambda phase transition of 4He must capture all of these effects simultaneously—a challenging task beyond simple mean-field models and perturbative approaches. This challenge was met by Feynman[3] in terms of the path integral formalism that exactly maps the interacting quantum system of interest onto an effective classical system of ring polymers[4]. This quest for an accurate description of h elium[5] has given rise to the widely used path integral Monte Carlo (PIMC) simulation method[6,7,8], one of the most successful tools in statistical physics, quantum chemistry, and related disciplines (We note that Monte Carlo methods in general are applied in a gamut of different contexts, like solid state physics[9,10] or the investigation of magnetic p roperties11–15)
We have presented an extensive set of new PIMC results for normal liquid 3He
Summary
PIMC results have been derived by introducing the uncontrolled fixed-node approximation. We present extensive new PIMC simulations of normal liquid 3He without any nodal constraints This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor S(q) , the momentum distribution n(q) , and the static density response function χ(q). An accurate description of physical effects such as the lambda phase transition of 4He must capture all of these effects simultaneously—a challenging task beyond simple mean-field models and perturbative approaches This challenge was met by Feynman[3] in terms of the path integral formalism that exactly maps the interacting quantum system of interest onto an effective classical system of ring polymers[4]. PIMC-based data for S(q, ω) have given important insights into the connection between superfluidity and roton-like quasi-particle excitations
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