\BOOKMARK [0][-]{chapter*.1}{Abstract}{}% 1 \BOOKMARK [0][-]{chapter*.2}{Zusammenfassung}{}% 2 \BOOKMARK [0][-]{chapter*.3}{Contents}{}% 3 \BOOKMARK [0][-]{chapter.1}{Introduction}{}% 4 \BOOKMARK [1][-]{section.1.1}{Birth of a quantum era}{chapter.1}% 5 \BOOKMARK [1][-]{section.1.2}{Quantum engineering of materials}{chapter.1}% 6 \BOOKMARK [1][-]{section.1.3}{Optical lattice as a quantum emulator}{chapter.1}% 7 \BOOKMARK [2][-]{subsection.1.3.1}{Optical lattice}{section.1.3}% 8 \BOOKMARK [2][-]{subsection.1.3.2}{Single particle in an optical lattice}{section.1.3}% 9 \BOOKMARK [2][-]{subsection.1.3.3}{Bosons in an optical lattice}{section.1.3}% 10 \BOOKMARK [2][-]{subsection.1.3.4}{Fermions in an optical lattice}{section.1.3}% 11 \BOOKMARK [0][-]{chapter.2}{Quantum Monte Carlo}{}% 12 \BOOKMARK [1][-]{section.2.1}{Quantum statistical mechanics}{chapter.2}% 13 \BOOKMARK [2][-]{subsection.2.1.1}{Feynman path-integral formalism}{section.2.1}% 14 \BOOKMARK [2][-]{subsection.2.1.2}{Configuration and worldlines diagram}{section.2.1}% 15 \BOOKMARK [1][-]{section.2.2}{Markov chain sampling}{chapter.2}% 16 \BOOKMARK [1][-]{section.2.3}{Directed worm algorithm}{chapter.2}% 17 \BOOKMARK [2][-]{subsection.2.3.1}{Local updates and non-ergodicity}{section.2.3}% 18 \BOOKMARK [2][-]{subsection.2.3.2}{Worms and extended configurations}{section.2.3}% 19 \BOOKMARK [2][-]{subsection.2.3.3}{Updates in extended configuaration space}{section.2.3}% 20 \BOOKMARK [2][-]{subsection.2.3.4}{Updates in configuration space}{section.2.3}% 21 \BOOKMARK [0][-]{chapter.3}{Thermometry}{}% 22 \BOOKMARK [1][-]{section.3.1}{Introduction}{chapter.3}% 23 \BOOKMARK [2][-]{subsection.3.1.1}{Temperature determination}{section.3.1}% 24 \BOOKMARK [2][-]{subsection.3.1.2}{Physical system}{section.3.1}% 25 \BOOKMARK [2][-]{subsection.3.1.3}{Single site addressability}{section.3.1}% 26 \BOOKMARK [1][-]{section.3.2}{Fluctuation-dissipation thermometry}{chapter.3}% 27 \BOOKMARK [2][-]{subsection.3.2.1}{Theory}{section.3.2}% 28 \BOOKMARK [2][-]{subsection.3.2.2}{Window sizing}{section.3.2}% 29 \BOOKMARK [2][-]{subsection.3.2.3}{Experimental imperfections}{section.3.2}% 30 \BOOKMARK [1][-]{section.3.3}{Wing thermometry}{chapter.3}% 31 \BOOKMARK [2][-]{subsection.3.3.1}{Theory}{section.3.3}% 32 \BOOKMARK [2][-]{subsection.3.3.2}{Advantages and limitations}{section.3.3}% 33 \BOOKMARK [0][-]{chapter.4}{Quantitative simulations}{}% 34 \BOOKMARK [1][-]{section.4.1}{Mimicking the experiments}{chapter.4}% 35 \BOOKMARK [2][-]{subsection.4.1.1}{Momentum distribution and time-of-flight image}{section.4.1}% 36 \BOOKMARK [2][-]{subsection.4.1.2}{Density profile}{section.4.1}% 37 \BOOKMARK [1][-]{section.4.2}{Beyond parabolic trapping}{chapter.4}% 38 \BOOKMARK [2][-]{subsection.4.2.1}{Quantifying error budgets}{section.4.2}% 39 \BOOKMARK [2][-]{subsection.4.2.2}{A first remark of waist correction}{section.4.2}% 40 \BOOKMARK [2][-]{subsection.4.2.3}{Corrections to parabolic trapping}{section.4.2}% 41 \BOOKMARK [0][-]{chapter.5}{Density functional theory}{}% 42 \BOOKMARK [1][-]{section.5.1}{General formalism}{chapter.5}% 43 \BOOKMARK [2][-]{subsection.5.1.1}{Hohenberg-Kohn theorems}{section.5.1}% 44 \BOOKMARK [2][-]{subsection.5.1.2}{Hohenberg-Kohn formalism}{section.5.1}% 45 \BOOKMARK [2][-]{subsection.5.1.3}{Kohn-Sham formalism}{section.5.1}% 46 \BOOKMARK [1][-]{section.5.2}{KS-DFT for fermionic optical lattice}{chapter.5}% 47 \BOOKMARK [2][-]{subsection.5.2.1}{Lattice translational symmetry}{section.5.2}% 48 \BOOKMARK [2][-]{subsection.5.2.2}{Simple cubic lattice \(Oh symmetry\)}{section.5.2}% 49 \BOOKMARK [2][-]{subsection.5.2.3}{Face centered cubic lattice}{section.5.2}% 50 \BOOKMARK [1][-]{section.5.3}{Remarks}{chapter.5}% 51 \BOOKMARK [2][-]{subsection.5.3.1}{Validity of Kohn-Sham density functional theory}{section.5.3}% 52 \BOOKMARK [2][-]{subsection.5.3.2}{Kohn-Sham band structure}{section.5.3}% 53 \BOOKMARK [0][-]{chapter.6}{Magnetism in optical lattice}{}% 54 \BOOKMARK [1][-]{section.6.1}{Introduction}{chapter.6}% 55 \BOOKMARK [1][-]{section.6.2}{Ferromagnetism in optical lattice}{chapter.6}% 56 \BOOKMARK [2][-]{subsection.6.2.1}{Probing ferromagnetism by Kohn-Sham DFT}{section.6.2}% 57 \BOOKMARK [2][-]{subsection.6.2.2}{Inadequetcy of Hohenberg-Kohn DFT}{section.6.2}% 58 \BOOKMARK [1][-]{section.6.3}{Antiferromagnetism in optical lattice}{chapter.6}% 59 \BOOKMARK [0][-]{chapter.7}{Conclusion and outlook}{}% 60 \BOOKMARK [0][-]{appendix.A}{Implementing quantitative simulations}{}% 61 \BOOKMARK [1][-]{section.A.1}{Optical lattice bandstructure}{appendix.A}% 62 \BOOKMARK [1][-]{section.A.2}{Expression for finite time-of-flight}{appendix.A}% 63 \BOOKMARK [1][-]{section.A.3}{Obtaining time-of-flight image}{appendix.A}% 64 \BOOKMARK [1][-]{section.A.4}{Obtaining density profile}{appendix.A}% 65 \BOOKMARK [1][-]{section.A.5}{Fixing "426830A N "526930B \040by tuning chemical potential}{appendix.A}% 66 \BOOKMARK [2][-]{subsection.A.5.1}{Initial simulations}{section.A.5}% 67 \BOOKMARK [2][-]{subsection.A.5.2}{Tuning chemical potential}{section.A.5}% 68 \BOOKMARK [2][-]{subsection.A.5.3}{Turning on measurements}{section.A.5}% 69 \BOOKMARK [0][-]{appendix.B}{Energy functional for repulsive Fermi gas}{}% 70 \BOOKMARK [1][-]{section.B.1}{Energy functional}{appendix.B}% 71 \BOOKMARK [1][-]{section.B.2}{Analytic behavior at polarization limits}{appendix.B}% 72 \BOOKMARK [0][-]{appendix*.24}{Bibliography}{}% 73 \BOOKMARK [0][-]{appendix*.25}{List of Publications}{}% 74 \BOOKMARK [0][-]{appendix*.26}{Curriculum Vitae}{}% 75 \BOOKMARK [0][-]{appendix*.27}{Acknowledgements}{}% 76