# Ab initio exchange-correlation free energy of the uniform electron gas at warm dense matter conditions

 Title: Ab initio exchange-correlation free energy of the uniform electron gas at warm dense matter conditions Author(s): Groth, SDornheim, TSjostrom, TMalone, FDFoulkes, WMCBonitz, M Item Type: Journal Article Abstract: In a recent Letter [T.~Dornheim \textit{et al.}, Phys. Rev. Lett. \textbf{117}, 156403 (2016)], we presented the first \textit{ab initio} quantum Monte-Carlo (QMC) results of the warm dense electron gas in the thermodynamic limit. However, a complete parametrization of the exchange-correlation free energy with respect to density, temperature, and spin polarization remained out of reach due to the absence of (i) accurate QMC results below $\theta=k_\text{B}T/E_\text{F}=0.5$ and (ii) of QMC results for spin polarizations different from the paramagnetic case. Here we overcome both remaining limitations. By closing the gap to the ground state and by performing extensive QMC simulations for different spin polarizations, we are able to obtain the first complete \textit{ab initio} exchange-correlation free energy functional; the accuracy achieved is an unprecedented $\sim 0.3\%$. This also allows us to quantify the accuracy and systematic errors of various previous approximate functionals. Publication Date: 28-Sep-2017 Date of Acceptance: 22-Aug-2017 URI: http://hdl.handle.net/10044/1/53350 DOI: https://dx.doi.org/10.1103/PhysRevLett.119.135001 ISSN: 0031-9007 Publisher: American Physical Society Journal / Book Title: Physical Review Letters Volume: 119 Issue: 13 Copyright Statement: © 2017 American Physical Society Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)EPSRCCSCS Swiss National Supercomputing CentreImperial College LondonEngineering and Physical Sciences Research Council Funder's Grant Number: EP/K038141/1EPSRC RAP Call November 2014Shepherd_2015_Ie494 Keywords: Science & TechnologyPhysical SciencesPhysics, MultidisciplinaryPhysicsEQUATION-OF-STATECOLLECTIVE DESCRIPTIONGROUND-STATEMONTE-CARLOPLASMASLIQUIDSSYSTEMSTHERMODYNAMICSAPPROXIMATIONTEMPERATURESphysics.plasm-phphysics.plasm-phcond-mat.stat-mechphysics.plasm-phphysics.plasm-phcond-mat.stat-mech02 Physical SciencesGeneral Physics Publication Status: Published Article Number: 135001 Appears in Collections: Condensed Matter TheoryPhysicsFaculty of Natural Sciences