Path integral Monte Carlo approach to the structural properties and collective excitations of liquid $$^3{\text {He}}$$ without fixed nodes

Dornheim, Tobias; Moldabekov, Zhandos A.; Vorberger, Jan; Militzer, Burkhard

doi:10.1038/s41598-021-04355-9

Path integral Monte Carlo approach to the structural properties and collective excitations of liquid $$$$^3{\text {He}}$$$$ without fixed nodes

Journal Article · Thu Jan 13 00:00:00 EST 2022 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-021-04355-9· OSTI ID:1839775

Dornheim, Tobias; Moldabekov, Zhandos A.; Vorberger, Jan; Militzer, Burkhard

Abstract

Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic $$$$^4{\text {He}}$$$$ $^{4} He$ exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic $$$$^3{\text {He}}$$$$ $^{3} He$ is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid $$$$^3{\text {He}}$$$$ $^{3} He$ without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor $$$$S({\mathbf {q}})$$$$ $S (q)$ , the momentum distribution $$$$n({\mathbf {q}})$$$$ $n (q)$ , and the static density response function $$$$\chi ({\mathbf {q}})$$$$ $χ (q)$ . In addition, the dynamic structure factor $$$$S({\mathbf {q}},\omega )$$$$ $S (q, ω)$ is rigorously reconstructed from imaginary-time PIMC data. From simulations of $$$$^3{\text {He}}$$$$ $^{3} He$ , we derived the familiar phonon–maxon–roton dispersion function that is well-known for $$$$^4{\text {He}}$$$$ $^{4} He$ and has been reported previously for two-dimensional $$$$^3{\text {He}}$$$$ $^{3} He$ films (Nature 483:576–579 (2012)). The comparison of our new results for both $$$$S({\mathbf {q}})$$$$ $S (q)$ and $$$$S({\mathbf {q}},\omega )$$$$ $S (q, ω)$ with neutron scattering measurements reveals an excellent agreement between theory and experiment.

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Research Organization:: University of California, Berkeley, CA (United States)

Sponsoring Organization:: Germany’s Federal Ministry of Education and Research (BMBF); Saxon Ministry for Science, Culture and Tourism (SMWK); USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003842; SC0016248

OSTI ID:: 1839775

Alternate ID(s):: OSTI ID: 1904861

Journal Information:: Scientific Reports, Journal Name: Scientific Reports Journal Issue: 1 Vol. 12; ISSN 2045-2322

Publisher:: Nature Publishing GroupCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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