From 9729e8697e3ef0f9256b81bcc27c457c13fdc86b Mon Sep 17 00:00:00 2001
From: Stefan Gehr <stefan.kerman.gehr@fau.de>
Date: Fri, 9 Dec 2022 01:54:47 +0100
Subject: [PATCH] progress
---
Makefile | 2 +-
figures/square.diag.lr.pdf | Bin 0 -> 1853 bytes
figures/square.diag.rl.pdf | Bin 0 -> 1851 bytes
figures/square.left.pdf | Bin 0 -> 1860 bytes
figures/square.left.right.pdf | Bin 0 -> 1564 bytes
figures/square.none.pdf | Bin 0 -> 1145 bytes
figures/square.right.pdf | Bin 0 -> 1551 bytes
figures/worldline.pdf | Bin 0 -> 13108 bytes
src/qmc-loop-algorithm-report.tex | 166 +++++++++++++++++++++++++++---
src/references.bib | 28 +++++
10 files changed, 180 insertions(+), 16 deletions(-)
create mode 100644 figures/square.diag.lr.pdf
create mode 100644 figures/square.diag.rl.pdf
create mode 100644 figures/square.left.pdf
create mode 100644 figures/square.left.right.pdf
create mode 100644 figures/square.none.pdf
create mode 100644 figures/square.right.pdf
create mode 100644 figures/worldline.pdf
diff --git a/Makefile b/Makefile
index 9e7a88d..4b7f76f 100644
--- a/Makefile
+++ b/Makefile
@@ -12,7 +12,7 @@ build/$(name).pdf: src/$(name).tex $(refs) fau-beamer/styles/beamerthemefau.sty
clean:
rm -rf build
- find src/ ! -name src ! -name $(name).tex ! -name *.bib ! -exec rm -rf {} +
+ find src/ -type f ! -name src ! -name $(name).tex ! -name *.bib ! -exec rm -rf {} +
show: build/$(name).pdf
xdg-open build/$(name).pdf
diff --git a/figures/square.diag.lr.pdf b/figures/square.diag.lr.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..b2f0270ab9bc0b4ad7e41b0dde8fb2f3fa5b3f85
GIT binary patch
literal 1853
zcmY!laB<T$)HCH$-THRjZ!QxB1BLvgEG`=x1%02?y!4U`1ycnBg&-~k1qFS#%$$<c
zA_aZ7oWzn;m(=9^lvFM|JFeoAqSVA(u8KLvAqEUivCayK8LQGW^0Ly>mQ9#*I+UZO
zEy0q5Q{<ArNq~ob*oE~5!38Iua~)ZHKxUD`1a5}r7s4C3Qu9)v#-!$@fE)m_6+|m2
zD3}?5q(K~Gxa+{~ajhtE4=zb8Nma110SSQIm}sB?a=Wvmf}w(ba-xEvf}I^m4npcj
z_$OthCYONKRG2B4f&8YRUtz9b4rbZefjk6t0!R{ME66-(SQr|Bl!45{8W<o4gj5!!
zD!}Xks|+qpDgg_+<rn3GMVy@SD-@y?K!zEbDHxh5#Dax`Qj7CTi;`1|6)eHlAcw7L
zw=GwLfk^ZB@~$}x_Wipq%+cgrD#9Kp$kP7m!PnfW6IulJx%4dB=V)sDZFYpj`zhQN
zpRT6KoA@OhjPNwFQaQn&7#Kb6R&BDSu|$ufCvRp8*EjwC?86Nn6XUKe6;lHRF=`Be
z{R;BGf`Wpj1xOym0l5rBLqc4i#3-<{gP8*gZ-_bYgl1?2_BALFv86PSI8_4I&=717
za_DM5F$!Qfs8G)O*M+(DOOl?lZ8EoWa&mHO(Sj-B0_laW$F(G0NNOx8kd)H+p(Uav
z(X>_KMdU0g38~qQmM3?{uvLkvsd2R}t7>zb#<kOc&ErahqPt>*;sosp+zhY&i-Cg=
zEqFn`1%&`8cr9VU0(Kinl+y6EfM*p2eMqSJCuIefK++#9HG}dKBy0OA7=n|aTV_#l
ziGm4~jX%5F_HN{BG7xbs-}gvw-K9ki9#U)uihOFzc1f}~>9;IZ)iwR}eVgfyy~RcE
zcS}Ynv0VCXC44E{Ua0H=r@(;;Q3nnxEZ%V;`<3+HgNL=*=DlBSlpHFm7x&CH@PTCW
z+OY2RQ8NGUp35+I?qF!FufCY~>e<?tQ|BIjw;}IW&ryq8E55E2-n+ap<vL5`^^f~i
zR?n3@@kqdY??0wx=B6p2;6w{<kY7OotDvA@Xlf2p0OA=U7kD_s36xl2;baUA8&EhI
znnOAG1IoAGmiv%_K->3!UFDlyJ>E5iiWFXSjd8hiMRChQwxyb$GJn2r`^Y?9`rhv6
z@8sB0V-~%6Ez)%=XJ?Czoi+2$>%E+k3_CZM9^m9^Vb;@(+U+iV@MhN3j=kky7aPe{
zE?rxmaM0M$wXSy~H@9Z+t%|#`xuPwfeFOJguUNeJ^~T(4?y2w2ZwhdF_(%Eeazlsb
z^`~}~Ene)nFH$3@OZ04~+TKGmDqKQp;;T=uDZNsDUB#xek$raJ3s(K*u3tgngcgvX
zzyJjuC?G8m2^TZLMFgd$fx`!y+|13uJY0D@II}8M!O#+{CR`!fP{ByS2wE=Y=a+y=
zNmxDPnU|KYU<j%qf<VPJ)O{6mk`oes{GZ?1*x%UL+1T9JI5APT;{m&%aRbX@lL-l{
z7=+H4JLoVAD6&5K*4*KxaPSk8%O7^h1ME{+gnW8(+8hkc_}SPP?tJFBkLm5=lEk8t
UilWpsE<-Z|3ocbvSARDy0G`iftpET3
literal 0
HcmV?d00001
diff --git a/figures/square.diag.rl.pdf b/figures/square.diag.rl.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..827ba3ce1c91f4ffcc2cebe8699374da87325d8b
GIT binary patch
literal 1851
zcmY!laB<T$)HCH$-THRjZ!QxB1BLvgEG`=x1%02?y!4U`1ycnBg&-~k1qFS#%$$<c
zA_aZ7oWzn;m(=9^lvFM|JFeoAqSVA(u8KLvAqEUivCayK8LQGW^0Ly>mQ9#*I+UZO
zEy0q5Q{<ArNq~ob*oE~5!38Iua~)ZHKxUD`1a5}r7s4C3Qu9)v#-!$@fE)m_6+|m2
zD3}?5q(K~Gxa+{~ajhtE4=zb8Nma110SSQIm}sB?a=Wvmf}w(ba-xEvf}I^m4npcj
z_$OthCYONKRG2B4f&8YRUtz9b4rbZefjk6t0!R{ME66-(SQr|Bl!45{8W<o4gj5!!
zD!}Xks|+qpDgg_+<rn3GMVy@SD-@y?K!zEbDHxh5#Dax`Qj7CTi;`1|6)eHlAcw7L
zw=GwLfk^ZB@~$}x_Wipq%+cgrD#9Kp$kP7m!PnfW6IulJx%4dB=V)sDZFYpj`zhQN
zpRT6KoA@OhjPNwFQaQn&7#Kb6R&BDSu|$ufCvRp8*EjwC?86Nn6XUKe6;lHRF=`Be
z{R;BGf`Wpj1xOym0l5rBLqc4i#3-<{gP8*gZ-_bYgl1?2_BALFv86PSI8_4I&=717
za_E|NZ{%t)5ODtfyQ}74<@MD;`yB*iRxP&ZXi~5eVXu$Z_VAEXRGFx-IzQk{(_5wE
zVpq--><|83wY;!tLxQSkiN}TaN-@(Hh1I57dRkQU&uJ5m+O+G}@kYjpO17{5h=D^7
zEp$Pi1qA>~=z^UF5~VbFE#NstK_3!m{z+NEC6MF?OU$6`1j*Tc3Wnem=$2VjT%uqC
zW#iB7w!ItqnhZo-%lAFfTX$)ZgNGEGfg+#UvR#twP5LcMRdr22ecxufV{dWM``wZe
zN-URtTM1vvwihaUz$tKGLeznS3X6AK$bKdL_uye|wt4SY8zqN|>cu^C4SXQkyf&<R
zeU!}qyXP{@ojVvB>#Hy3y?VCx<<z-{-)+eI)pOM1){3tyh4(IROu5bydHv&lmDO`4
zPdpMZ-}{egnYn2SD3PHBH^{G`fK^aXFf=s>DFE>dk;^-r;RH&nuy8Vlh7Bm349%e&
z`~l_LZ_9niK%njWzpnDlt{(52LPZKMy2iNNxuUpbA=^?-Pnkd8w|!)uE`4wJ^LKJ=
zsWFS*ycX#?m9w+O#?G2~=k;DrNrs)9OAl~zwJ_^xM(uW&K6o>0YRBI4uZxZ3DwnP;
zPdI37=vvpik(*mH_*TW;*j&+;&%S|su2(Ex{CZ<<HTTqa=Qjm7J^Z8mcDbR$^ZHY}
z$`&tn+!v`4)FpbhQ_bb+j0%^Kn)vF|Yf7(_Usti|Y-FFE_<~j6(e*PZoX`Ri6d0hO
z0|lgoB}f5?XNZ~LB7#!Wz~KW;Zsw+79<Hn%oLQBsU}y<e6Rr?#s9>aE1T7Zx^GiU5
zB&-_p%uCBxFa%W)L7>ta>b{CO$q5NR{?G4h>~C!BY;109oS3NF@qk^>xPfJ{$%KSe
z3_@qFJL)hCD6&5K*2pn|<#e&YNB$HB`2Zmg1H(;?S2pf6Heg`5W65y?<SD4B(5j%g
YB(bQZq9`?u%h1fgoJ&>J)!&T^07U<7hyVZp
literal 0
HcmV?d00001
diff --git a/figures/square.left.pdf b/figures/square.left.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..9025b68803f9c70f80c0b8e560b8c3d475cfe335
GIT binary patch
literal 1860
zcmY!laB<T$)HCH$-THRjZ!QxB1BLvgEG`=x1%02?y!4U`1ycnBg&-~k1qFS#%$$<c
zA_aZ7oWzn;m(=9^lvFM|JFeoAqSVA(u8KLvAqEUivCayK8H>^rQW8@#mrR&*I+UZO
zEy0q5Q{<ArNq~ob*oE~5!38Iua~)ZHKxUD`1a5{#P2uHSsd*_-V^Z@{Kn?)e3ZfMh
z6wC}j(jbm8+;w30xK@<72bUz4q$=3hfCNBpOf*mcx!u`O!B9azIZ?q-!OjjO2O;$%
z{FAa$lS{yAD$EqjKz>uuuP|3I2ea(#KpuiR0VD~s6=WVXEDQ}m%0T8}4GfS2LMjVV
z6=3#&RR)(Pm4F4^@{4l8B2G^E6$;S`Aj1sJ6bwxjV!^^esm1xFMaikf3YK7Nki%B{
ziBSN<L4|VGzb?$JUy}5gZH0@Cm5sSuixx}~7f3I3J+3A3LQ-Q%fuxki4=oWbiKeX*
zFCu42Nl49Zv^=>prmd=NnuDaRaxyoov#_l)w>L-Xx_~LG1l9<gaNTyyL63o>T(Jri
z&ZyA<_An?A6ciK;4U9nwKs=E9Kr|%W^+}8fJ3E*;piqaH15a*-Mqs~#f)ZPL1Bp{5
zhz$+F_8^C`YPTU*gMk3c@9Lxb9_%?Sc~P9B$#shecc8!#k)(&;dnYD#C(i6<k$3J+
z5`1HBxh?7}kN>V+Tbh?i9%||hx$wB@nahrki^5VPl{K>$UzoJ_bH|U+8<D-j%1o?P
zjF+#9{sws)Eqp<~1%-fuf`X+bNFKxiyA8ykG<+@K8Ad@L5^DZQS-~ZcR0vDcpj-vX
z;C>2*;DqRwSyWu2U;<_1&-Auu4Y`{QL|7i&jW6^L_f6{3WntI#Xm{Fp*Nc54f1%-|
z8A1PRCyQ9$JHES|Nhgr&X6;<gn_HzhtUs`D9K5ilp?P6%!NTh|LVq>4tF!I%=Z-U&
z*?f9RXR`&D&Ev$i%a4ZZKG}a;;%%CSsMCr4dsj%`-7_n1Q}K<r*L%-L^eooB`tOy?
z`;E)Dtz?>(`se<ntLMI?Og!#;K7PhlQ(sVUq6Ig|ub_YhC1+D}kOC0T5V_dH8BU<Y
z3JWJ=XxM<l$<Q3i!5>h*{kGhP3<TP~|LZE>?CSAODO9BJqHB!Hohyo47P2kX^pyGY
zecMOo>C*RhKYu63mKw9@&1;daQ#m_ZZ0xL=cV6%1lw{bsx%2=hR|~VAX4GzX>4P`3
zrgrQt|GL;nu5#(x@`QuNhOTwJ8@ahPgKt&bjm;Hp`Rp6G=X%BB#jiK!R&!5%cYafV
z)5AZ?Z<iZ7Jg+~st8DRN$9<6+L0zI}JJmw`jvY~6^yv4k=(M$q_w81D=*eSqgU4B4
zf2r$NP&lClBq%UIK?e#*3q-=jOmGoFscGQwfhIR|+@S@^+rgPtsS1XcU>)HK(S`~}
z3P#Y<F+aaV!4Om^Ln6U5FD)Nbc7kdr<XoJbknrRG{LaSy#>URZ=ElZ}iMkyR*aeLn
zSQeX1NLa-zbmqH*j<J9u|06$E!LJTYPh}@0q_RpLV4uPw<kOS$%)!vio{f#+>@E&z
cOn(=bBo>ua6s4wd8JZcIaH*=g`nz!f0OpiwivR!s
literal 0
HcmV?d00001
diff --git a/figures/square.left.right.pdf b/figures/square.left.right.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..630b0af288346c50b2cef50470ab7967c2151747
GIT binary patch
literal 1564
zcmY!laB<T$)HCH$-THRjZ!QxB1BLvgEG`=x1%02?y!4U`1ycnBg&-~k1qFS#%$$<c
zA_aZ7oWzn;m(=9^lvFM|JFeoAqSVA(u8KLOeH*!$9C=)R*Bt%RursB&`pvf{g@`rN
zk`%d`Dozx(*6m9S7vz>SGN|<FaEjqBy*y8K$pmIUWnaCuYj&>RwfKS2;%dH#dn+e|
zY=~XR$d%)HmWSUxd%pHtegUyLo~+V7@1qY{cHR15xn|8xPIhmJi<9hyosaNZi~Nf2
zxwAZf<Fffl3&n2)>OAL4%}as0Dm5<!<R6eHK(vB_f}yb`NFKy9hWi%mKi7&9_u!Jm
zl2ip78;}6V&xr;Kps;XuR4`P~Pfk=YRIsxH$w5f{2>+z4)Z`MdnhG-oGf-H8RM^?U
z>;MUY>;jnr4N*&wDv%*qLlk6dNM%8)0?cr*%HYzZ60o3Keo-!1#K|eYLLpkgK*2!4
z&|JaLR3R2D9F$s|Us{x$TC89Jwgx$ZRJ#qi8Vm$jepese_h3)Ap_;w`3-?wL?m$77
z?u>`udrxiBIlN&aOa3mdn<_W-gtjd;KKIyfmEYY=2}PX<4_02KFS|L~olMH*&#-G|
zd$jq!TR5$k|Nj(=@GluFm$F~e6;lEE8a3oWo(1_I6!HcJAbAiE<Telu321#1Lmm;j
z=I|I)(1!$?e^OR(2_%G|!EFc%B1j7MQ!oSvl3Qj`afyNnl#M@C+nzP#Z!!>Jc`!G=
zuv>eJXyBwaMxT!6PDk^{7anvcE?lzI?cd&9-oEco?^-iX^XPoD&8OwfqPP~`3Z|BX
zj5!AnUU0RzTpY0V--CCZjpCVsQ+C(#&0Fpx<D&VYqrF!yJ$~zn|97utm^+>laQgSw
zHTLDJt1B-0C2o%ovr9DVyLRQrYURD{^LB0HiwON#?;d7-dGb-SysCdpi{eaULBWX{
z++fdwLKYO>rWPOtAfBNiF#!e2{jh*Ch6WBOpbX8S9Q+~W+rM$$Ap;)Q?{!D-X0%SZ
z;npDMq_aUmtmQ_7qE=w1T-GWTo<Fv^75p13c6{4dD-p6G;nsD|mSsnaIBRRl#H#Y8
zq`4WYp05*B=ip$EDcbU_->k9ws+REY2kZN9u}#@pc(7UY{8gT(x=Z!+ww%ip_9-te
z4Y4x`{Te5{#&h5CZEy3}_|{LGs&VkA^RE5J80PNRe15yvQ|xJ)qRJsBdl#d}CudZ+
zg#6wAZCd2)lz011R){h4n;pKut@+dS11O--LJ|}jps)jlq$ND%8p4VaP=<yixrm_D
zG;jbx6P%eDn1`*n1ZD2v%&JrcLx`Gig=j+sBLyR9-p$W1Q7{CRN|0Fa%uCBxFf_u*
z$H@r^KmO0}Y@FTL*x5L@v2o%<{f-Chg6A7ql9eVT+~QX{<;c=;x`xrkhW+IOHZDd^
rHMcO$1rn<jnVA_Ti*q<)dbYSEv8be?C^e1C(Adb5OI6j?-;E0Zw>}<J
literal 0
HcmV?d00001
diff --git a/figures/square.none.pdf b/figures/square.none.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..6273d72b2d3e4575f5e63e46c61a9b5151befea4
GIT binary patch
literal 1145
zcmY!laB<T$)HCH$-THRjZ!QxB1BLvgEG`=x1%02?y!4U`1ycnBg&-~k1qFS#%$$<c
zA_aZ7oWzn;m(=9^lvFM|JFeoAqSVA(u8KLTy^dUm0(e}$TON%$VBz`t{eN{04!x}D
zOS^+y1!A`7?b-Km`ULZqL^ZZ!b955cUfL{v{MSU^h`H7MpPlyXbIRTQMDwxuHPdgp
zmwB{43Ml8@NHBHM6_1+yN-#7e--z!R|M{mA_<jp3vq?VT|211`1y^cb3e@t{ycCeL
zL2d=n3JMB_h9)3+5YHIyDX=$OD@xphOA<>`6>Mxk0wAv?8YqCg?ChvusGy&ms9>mI
zX9tqAvjh1MYPuQR90mQ5%7Rn{egCAa;F4UBLRe^-!$ZqY!4NFrmRVF>qF@4L;}1dG
zUR&-%1|qKC|8?!&aZBY`ztf8gTt^)zyi(&^Xt%^WXj0gl{pOul-p)O|_dVAJAI&G*
zD;1uI|5aLZz*wP4*|@2Bq3<J~^Ks$dnyUkNV%B}P-kIvUXNE<G(}RgkTTPQ!RGp~b
zURWlzAf)BQ{=F&UrM%ZNAGhzgeYV>!u|!xmr2Wdod$sPl!LE_hUe<fx^INCf?|X~q
z7x&zH(@;=gq6Rj|tDxWo1-7X<NFKzqAR>?q4Ut007#cF5P%<=wa_|R}Z@=woCPM+&
z-+#Jp@9ds%hG&IF(&FAdZgOQ=g4Z^%rEXT)Sn>bg&X3Hut&88CNt`e%*{O@uNqB3_
zp*R1l*f(!p>&?~h^W*atW|o%tIbK`%zUwt#%?j;^<#}HHSZUR<UlIpqrB`*mnp8Yr
z?AVkoz1#NxP<ttGdsp2xm-OO_gxl|CN&U7s9ku1b55>RP1`fybPqpVIZ+6}q$<evt
z!W@r|<;jl(1OL{&)!e-8<~^tA4@zuuIc-bpfB$kl01744Py~ksDBwWBXkh_T0OA=M
zVT5BuP-+@DcwiaR0?fmfD?v#*II}8M!4ML<;R?})3PuV>v0xoR`S~RZh6eCB@XSlg
zSFi+gk+XAhLc)*#^E(@x8yh<tdm9@kKIH6pz%KZ_fn_n@goI6Of{hBQG7fAL5|UE#
qSh@_)CnPX1JiEwx7UTs~KNgoH7L`;KrKWLN8X0h@s=E5SaRC5qe5q~#
literal 0
HcmV?d00001
diff --git a/figures/square.right.pdf b/figures/square.right.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..483a993496c3880ba0648afa786e0a1579af9851
GIT binary patch
literal 1551
zcmY!laB<T$)HCH$-THRjZ!QxB1BLvgEG`=x1%02?y!4U`1ycnBg&-~k1qFS#%$$<c
zA_aZ7oWzn;m(=9^lvFM|JFeoAqSVA(u8KLPy$89N40&AM|Lpq7xOs9}?(TBOhz}d8
zMEDmeaVV{3|NDnm*C@qFLhZc6^;37>y78eeh{YWW?mZVs~fmsBgLTTqNk=^~D#T
zD;^hKaU`_oMq=AluF{ChNvqoTFKUapa7S_>Pj2d-e2avlFzs9WFLu1B<D5O+XC3Rk
zFN$ZlQu9)vE=kQx0r>&sa1gDapkQcZ4w47)jNv{6`^mMU#67qqu_RT&#s(w+@@Jxf
z0?7Z)jtYhf`pJn3h6;9eAUO!BAK{;rm6}`vR#Rc7U<L{wkP16Hm>nP?kX;~CprL39
zQUx*uYbb(j4XG?hRe%`|RvBEHR00-s%P-0Wi#R#uS13d)7$_Jh7@8><nkvMCg@aOy
z^Gl18Q;QWWz}6r~if*?dSAzo&%kMo&@dA^(mp|ubIq0N&)JcTpqLa>_ea{t7Z{Rr{
zr}E>{^%H3a%O)ptXQfp<y5dqMrOv?}7UbB?JxlM<RPn7!CyORMdlTCkBBx#_UM5zM
z;NUL1moY^w6Xa*qa0hu6<a-4L1xpK%G>8Lo7>I_1vObByjtE+Fc=RdgLqg0yDJ!@H
z5<JkbHUxzaB+2?I7=lB{EwiY&M8O2g#-EIB&l>VK8Hlhvm>XZ%t-Yn;&;^4A&O!sj
z7ilsa`y{4q%j}+5pC8@)xVG}U9=msoLs_(`;_e>(Lwq)jP6jHn77}e7=~d^FSKIBV
zPI~Zr%Og?iD-TjneOmRvRPN)3;7dPOx&D0r%}rOzsYT#ZzWyt>@bzg^!rJd<-u=On
zE_N&E`TD*u^VFq&nI&94@}D_!>x@pFt{pFba?jpn8UzYW)W8P&6%??bRBj4S<%WjD
zgcB&Y!@|iJ8aAMCGBk&B@CTG{|Hi&U20U%w?T+rh_-e_KGJXM$jR%_Y96NX=770y#
z;paQGrE&XyGnp4+{QLjj{3j8zA;Id3l+)#;txa}zRor{c*Y>h9{C&DkP@RK=J*H^O
z$M1TL-CwPQe?M6N{TSPn-ok^;qUW#jJk?!lr?>T7rnFCev2Tdome8*;!fQP14wT(3
z&pA^tZK}q>pT4{HALE$&KlogE^kkh=Z-YEqTE$#S|L**uFi#+K{q=c9(v#2h=Nr#E
zdSLNci!a>T0j}S%ge53EU}0%#1X2Lv8Nvz@P<Do-xrm_DG;k0>Q=A#@00U+1;LNI2
z1w%8ij&Ox&Lj@xRBWTXe&o5Ch1eHmUc<{_i%U3Wo!pOzR2?;;`&+lxU-PqXKIJdEJ
z;zQ+*2ke5|8(ESyCM4WqP%?6GF_@5G$Dp*Xxuk%(wSh%gS(`tgCv;{bBSWJA`&N)=
cP*YBENn%k+MNw)Rm!YwtDVM6MtG^o;0JkL}-v9sr
literal 0
HcmV?d00001
diff --git a/figures/worldline.pdf b/figures/worldline.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..8f0fc5cbd49521e91eb3be24cd5ffec0dcddb6e5
GIT binary patch
literal 13108
zcmY!laB<T$)HCH$-THRjZ!QxB1BLvgEG`=x1%02?y!4U`1ycnBg&-~k1qFS#%$$<c
zA_aZ7oWzn;m(=9^lvFM|JFeoAqSVA(u8KKp19tNrGT^!MSM(p_og03iZ~ScZJJZ3~
zCKj^s!_OTHb*E~GGIu@s@$Sv!b3Nzo^{w6TeM(5tkzn?{wtBZ#ONGkH&U+tW%k(b)
zf<v?I8yU;9+vGi(655py?o+$gp}VSz>*3@XVNrV;wytVABob^UEVjy3{mwayiO)<D
z{O>IY;B%F`-p#YRk9|)bOV@jc`|X$R2d`e7prk$7O0LMi$AwFE#R}6p&nHFA55H#`
zGHpJ)>+3hhPx|Z$=6(l--v}4?ai!*^K>d=MmjVg}kk>)9f`Wpfr7=hz#50D65ja#_
zD@xphOA<>`6>Mxk0-%seG*AGAptGZbp@M#LqJp7<ogGLHLh48OCuOB3mw?q&m?@Zn
zLRdk+!d$@|%Cb<ffU+zVETJqz0|i3^Fx$=!6zotpf;59%1+otsV}>9X;*K(q14Akc
zQWaqC0J%&*xHPE*Ea;YBlnWMda>}nzh*kjEX=rY!U}$2h5DS(FN-fSWElN%;RxmUI
zISAw$Xuws>SsLNnecM1_@9*$48>3IGS#t6D)&MVV+nm|aFBNml6Q@@sUOsfGKHgF?
z_3e}&$u1smB=%qYeCG1y6Z*YP?}~36eCu}bUHRw4x%z9BvR-$@ls{|gw7UP;z$(3m
zeXYo{6}p)b+t0o&TN=jo>F2h}?>q0lk(+PczW>AXjkOK4zXpFUJeyqen}sX)!!h@Y
zv)A`Mc^~}war(Yh55gCV*0hRWI9~mk!7uaEar^JN$-52)%iUbuxghtS?{Vi#1r-hN
z3$DjBTXj!c!y&~v)l6x{HL2JyN;zB}Ue1?h2+dvau7o2v;9M|=gh=NnmBylZDi<cH
zb58sGgmdk;)1RIwvpF+o%;Matb-q_aYU=7_;jGEidQV-Q=&;jDC}U+G%jv6%-4lcC
z{V%sZef4EwvFX996MLfMu4$aHQ?I&VbA4|>Xa0$$PBC_B%Ex)so;$pJV*GFa<UL_B
z%ocGR=hkTIi*DoIQ2Rgar?AYge-)7{3i;;jkm7qTaNV|Qj<eow&xKvg+V1n(m2OL1
z(9%~9O!^{PsCl?hEXSx;C{K}-Px1KyxyZ>JAX+SbGCPRg#Mg3>Csb1WT+hbP%4yD5
z3KH616i1jDTTF~wSh#JKSaR(l9p7)39HyGj4+yVT<5z8&!EBw{D|bWlX_bavcyLcK
zPobI@i_(=-S2s$$o{*Ng$lqxNrzN{snXi%;havmC2d0%8ibrI;%%@(M8F1D2YxMP0
zSy}s*(}gR~X{|TkwE4<~WCc?%&E`vdVOJWRdvX<@l}-_rxuO0vO5<HnVAp0}uk3@*
zf)*a%l%jh-V&kOaT^SP=sVP;=?K+ej!+p3cjsNg>j%ta0GB^73LwC<^)}D9y(9wIP
z{D+x*T(sY>vMRX{YteUp_axyz>wdDwoaK51%D>QL3e7v<i~`C$3JMBlW)>g?ARahX
zgBXwutxrY{cgxQMWp7Y+0cE!|T?1VM1w&Bj3eJ}(IT)1bA-2KGTtiT<2CKwc=z@%-
zRt^T0aX~0KSo?`l0K-9ra@M~t%&lLN^q6ghi;b0yxm$}COc57IFLXVwCGkR1V@ZLe
zl*SJ&5iN<Ptr9OHXGuv&&2F?jxih9stxD|}SDV|js%LF(Tsyf0_D$S4ud{KfQ=iiY
zCxvhYaRwGnv0PAKqs0cu)1ZI=6}JW^AO#?vA;^Uw26?ezX9qI~RHQ=8L4-3%j6UHE
zie=PrUOH*F-(d#<*WZ7;R%*6YzRBLFASC3vz(u6PU7)C|rRje9pE8j~$BC&oi?4q_
zcQaC+$+23tyx_0PhTlAM0z)0NR)yYRcJJX*%DB0JQOsx2<04}n?S%oEr<Ypq_)unA
zvg0;GqE2K{tN!)8KmR!R`_~EWVNu)B%3SbWccE(1+1QVJ=Fi~C-a1oLY5I<YSJTzi
zjwL;M`g`VoxowRXq9eYwrR&@Ec$_eFJo945JoR_UN1y!dTdzL*SLaUe6#~4GYx+I@
zF5V*enqz0u$Jp2g12r9iH}M={0c&EK9&md7c`d@Sb<?U}@f(f2#oD#suv>6Vu|3&u
zu~l8}pv2jdb?w{EeyC;WjVKj6@Yb^WX3-j-!aO^U`j26*Ns$#ZC4<izztou0)Ebqz
z!RJM-tlzEN!{#g4_ud9YC0e2Z#ULnF6%-VV4J<(lKs-ZGaDy0>CK^!f3o!?tXpBHL
zB7G7K$ad63W9xmI%OODI&iwT=^evvnT|X+Wk=nRa$3=7Fgx34z5gD_dU7h2!=Y^Jv
z@WwbN-pVf<599{t-bs;gR23_9X%>FBJK%JWUT^#i{*OC<Eow1c#@KGTs=I#UVt4Je
zHePGR#Xtdw8p2@jf`ULnLBSGHMuMCM5~VbN!EG9dL5L8BG%G;G9JV$mNSsQ=pOGO(
z17_+3-)tsBfwuQQMT@T->iaw~M`(o{*HVQq3+~RY5ZK?Pai!|T{r7LyZPl*Ih;%yf
zWM=xkvlj)g+<z{{#@+Px<VKBYCz-Vu3ms;RFv{{f`!2Z2Hb$azn>p(-iDdSjAKxT?
zE|4>;WptAF-gr-cb#Lz5J2`owO;eMb!Y!E0brSiGM47ceUAWlyMC7iITU<8I_OtoA
zBK)IXNA>>Xs^*jLi)}*n5<4c{l4*6cTOrQDxp;#I!?&&ww)FwBcM^gF9H;HNwc}pN
z-W!KsCU1=SzItx*F`v{N+p>V}Ij;{gPTt$3k#cZ}+M~^#+<CtJE=QD$BLeHbY>u1n
z{q~^1ug_UEN6)`vlWe_VcI`Tg;NE94%pt4mxwGTme{f38_b}h_H{sZm+_pc7QMdoc
z?Cku_X29CUfhEC!Vh<Ff;4EnhQUKzCgBrvjFU5c&oj|P$Qj(@?sB5TT1aARD#Ef(e
z6pXOfzJ{O_0CARrJ|tE7CuIefK-$327PS$m4uWKPKLtZjt*-BuSyWu2U;<_1?-<#h
zHRNtK5Mg<6H@?t2+}9+8`=BHDrG){P@|HH=a4$5RG$ZJL?PL+_d&hT|TSh3UZn|wH
zyvh5&(whUq3M|f-nfTa5ANri%nE!>n+@EJpN@nO&pEn0vJyt8(PpLR^I?TWOeN;#N
zPUBl=Cm6L%sBaE5-&JM$H|4p3%^K<X8zkJLv;JP4c<-^ps%)lfrGM6+$VzA1r15Ck
zbN%zjP5VL7gO=ezo&|*ns2(<j=XfJTk&4Kupwbr-F1Ru(yk7wdTSI4*md4yL&Y0lv
zYxUpf%-&;iV@HC<Gt<f~bIYQ(cFo=8yLR_h?xkFtR=EbItbFr(86&5FkAhAjC)cL;
z3QZkruU!+}I{WfU(YGDnX1|+VGE@5ZoU*20y?^(uzwc9DT=)KN{JXvBmCv7)pZo7`
z(IumpvMIeHr66ffc*&DvE8O=wISFsi>v_!a)S}Pgp88v+^!?LslqQH@eCM^4HRyW3
zr2V&3TV&MvW$d@v*(T=r&VLcH^Jbsx#-d5F)_uj&?Q?nrZVJD2y}CJV$8P&KkDq=&
zu_g2Jbl2lcj<vS8sqV0SX7{>q`-70}x6SiTJ3l(?y!eh>(H{@4n^LmEl0s7p+<)6|
z-amED?Xz$0<fVT<ZEPebQ_1xFXk~G>h5WhcpCA9($&fd}#=&f|z^2xgNd`iGJxdzi
zsHi2WwJzz1@G#U=T)LzwWRg~r^3@dao4#2dx;LF)dDvzu^e*W%nJjk6t8c>f6R)3W
zSh}{I$Si7`qnbbA`$<+KAH7N5PnbW67tQRMp#4Pa=Y$&1eM<3@^G}!>dF@lZKk@xZ
z{wM06j0+qX7#f>+jvZ#1!7=%Oq*}97%mcZCR?P*BjPF==UpTOs@8Eye&i<g>fcx3O
znjgwGjNA`ABRIMf4A-#fe`qs(z`XAP`#%AO#tmZE4pvnNHYG6Uv?SbMnXSmO%|WBZ
z(Zc0`_XbfVMZQOhj6Ml%P8!VGQ=C~toJ4OV@LzGXHE~cjaWvlIpuNS>y2L@f#L@iA
zfw&i~wHMg`Zjfhtz`%3Ju|hJg(YZh(u2uPi)E++fhY~XF!UaNp2L<M|ZGVtk!G7-G
z{0Ff+7!DT*>K$bNAije~`Ga8%)BHo}A1rGa;}3;@Fs)&}o*=TX_5FkDAB_Llc-|Dq
z*0FHr9k~Bc{fDHb3P*=WU|Z3Xz{c{0LURjb?)7TP^a~d#`8lP}>B%ZNSbafs`2s%I
zlHyI(`&ORwxjk>TqRNvHS%I1I^(xy<7du{`yklY7)DJHvIrO*8deYWryS3Dnby}0q
z#fY$gs70CYR=l>pBJ*_d=O;_uZG$(Pw`d4WHa@Iu;<r6@J2&^{lgwO~wX03mbj#N)
zUAHLM;>w1vl7U<gd(Y?j^PdS%*>Kj(?!uz=8Wu|uR{lwMJU(sB{aN4cc-?iiJN{<6
z(7NxZXG}UKK5fIzThli6I0PDfWL^E`Hq$3jzn%wQ?_Xcx%r$v!U~G_qc3JAV-u3eT
zT#Ps5=I5+lXP=UHna459cjEr-hiBzR-CBR<TvSfLk`3FW>K3L}yB?e`s?%VfmUi>f
zgr2k0?nh+rUzMk+|2A3JKc~V(Au~CnE3Y<ZM&hi%hf|JkG1^<>o|m`J(I91}Zq-H;
z#e+inIv+koKfAl}<*BHTE-h=UE5rYU`Cjn8_|L!fYoFSSORC?!c5YpAB1ZAfs&<pl
zo2-n&=WmIfE-AiQ*^{IDos>X##pRXEd*7_9YrQOc^X1agU-p-jz3xOtep%PkmgZYu
z{rTYIT*1w+N|VjEUSIfaTHo=;1q+$~R`>C|tjl~k@he~VtAv{K`u%;?b2scZ`}6(Z
zna<+&$JX&5{!HDGJW1JAHa%S`@`#;x_vFltkB({mn_vEFM)s{;N2YDtwd>lomR%Zw
zUtjCxT~Bz~v{B&Iwq#rO`_@}Lc6mR4qwo0OQR?eGRkup`E_<ooE`PhNX#O;VfAN*S
z<M#!Z-_vt;aw@qp*XRD$(^2)ir&|Z5Y03Y7zJv3;OCAqzf0uWuH^;|YQu3QSA1^DK
zcPHpw=DWyutjA+`OMD{a-)X+%zw^0Ia`&w0bG|atyQUOB`nA)1=l7lYJLaFfdt~O0
z36d#%k$yHO!;V|zPFu6;`j*8OzAKY>t+U^*b3bua@R{K^pLyYL4?W5$st>NJbe!K*
z`uSN<wrA(MeT50(+Y1)x<+N(JesWu{v-f)hzv_*O_h(*hcAFUaqj6i`U48E3<;Twm
zFAcc2<J5%Bw;lv^Zu__~?WVWb-rV_Zte<^${=9PN>c5SvYfFv?AD&&?BA&d>*4*Fb
z{R^vj_v=6Jz1hX(e%*BH()FTClkVN#p<CR$pzD&KRoP72KaHOs)JCP(*RL&p>bG?B
zf1S0bmZ<7JkNCyxb@h4F@6L;!hZh&S&AGp_tkUIWP3y(i@1EY0aqoJy_{k-XXuGEV
zjL=I##}Dp_`t*-umv*SV#z|+dsf(3@vaSjK-oaOt#}c{nZunn;;1lyhKdm|&l{CL@
z|KgD1Dc>&cO(~g@J9||ri*kJLgLyZ-u0}px67IkG=kq!2H*deu{c3Xj`P6U;-mi;3
zC(I0*y5b98SG=%F+ymaU`AatBW?x#i<nyvkkLHFgT&<Elw?et+`_=TdMlWQZ8NYeU
z9ObrU$;U$_OSLwidY7H5A9k{O>h!sJK@87dN2}fLzS8UJI_=P*MUNIOT2%Y^*jw#Y
zTSY`gt<0`1Dl8Yis(ZyXk2i4Q#}uZM%0KyfWL4Ntwi_^~HSK2Jy(y9XNdse1y>il=
z#?9M5KIDpN<$t*U!TJvu>n(noYCPDxVs9&hL_^~aG4mvYyhCRtnkGuLUX*CwDAE3L
zMnmU}mXkA@R?cX<xr4d*Lc`7(?LRY)FzGmJPfKPsOHejTG~Sk=y)DtYEJ3|2(fr$k
zxHm^@Z?ym2A<zDSf$x!Hjb!{m=L(7Vqrw$J{tpG_9W$;FyMMs^qi&7#{e#6n)N925
z_q=~tStGCiz##63_Yc9kp7{@!|B$Tfi+?cvhiF~z{RgHpNAo{g|B<UduwT*HI_|i9
z;34TB<$pNqm&vG#XasqshWJ&kT2LOSTDs`*i@PDNu`g_|O!ZqRrFEft<+N8TJnp`z
z{ZjXf;je7%1Ur{{fB9wo7gm<2l`h}>BKZsdmqM%A=N1;fw6U81Z=#)}_yzTsPP;nv
zmU+Jj+SQ}CT>C|EiE8aEJLmaJ&j<4VviZ71|3YYq>DSVtq|aBnujO@A`F*%`p~}X~
z=k3{-2J^x;DE{m--xT%OO2l^J>+e4}8D9q-c0N*i(D3y0Y?ZsaH%tEi`Ezp5?e&w}
zZkBv4sJwnpF>!_Bua90AUpf_Y-%@_F?o}=K&n0ILO-eD`7?Rf8yX^><@id+JFE5IG
z3Tu&&o<C(z?ELxWs+t!U_+M6;_WHZ}>uEoay5(H_5y$cC(Vv3L|CD##`xYy^ch=?C
zzov`4R4Ltf=D19J*xHqE-{k3Cefs^1#Mwjl?4pZz-?*9d+HOte*|q22T=29sH+eN@
zUE<-@hur7hb_&<OrE^m5bCzvDeA?@3*DV|Tuc}Ay;@@Vz)HUpN)}d4Jcb0tY<BR@Z
z^Fcbk$8oCdt&1-wO;CKl;+)@kZG$JzJA#*nb*3LRat@7~8oK#*m{G#Dn@b+}?9<Gj
zzR#rh<Wi>VT@t~Ks@@lc0`{spPoDQ+=C)Ar=@X|+(v;YA++mlB=~j){4u8+i?u>rv
zir)_czdZ=Nc=6t4ZR=BOd0T^J8Y8Fq{_9a)p3}o?V7ESC)=sx+2dB?UdDg`>IW$AV
zn_p-t&%GTg*4ay&i+c)Z9X9>+^Vu1#$JJ*dGwtFd3wH(tD$DvkT>oTR`pm7Y-P>M2
zw=%g{XI~t?K0;dRz3Q1SJC6K#-#72~g5^fqN3_J$Pc8B)Uw)O-w>s-p|JsVmyan||
z85<-7MD~8->|L_YqWNJ$d}($6x}E!$Eq(jMHz}bo(bDYa<!4{C9(%HSKe7HMpQovJ
z`mEOV)Einw+O2H2*G)UO<kpAYi=C&Lj`;tG*<7BKv8;Sm@+r}<sWY`&j?JDa^2yD<
z`Ji)scg_xjy}s`PS8NxP3BF<f`16^6FQdPlmYuwDhWXU+8D6b?*~^kmj(uXan>q9R
zbIm$Y)!-?`x6S6*T)ADaBzXJUn6eLi%^Re+i%VBOcWZNBs`<r|t=VyMzLA(z>H5Fb
zFV0R>icAS>k1fr*^iyzJ#nqjclw4OuzRUZWbh#}1U?l78qt?q^zFbLvD?a1$@t#fW
zH(NyO=e{!d8s@eBbiUQct#AC^iSPQi{JGE5d0qGNKF+UpE)I@cYcQwe^X6pX%bSH;
zbtTWHyDYC)?2^|0(Pa7m{L&?7R^5)vo*(=F{pLNBbFXyNuK0F6`DXZEF|H$W<puNW
z8B+RRyvNdm0CfwXJqTk1Lo<*H5ZA~OK6L``LKx#8O+lVtik;}2eb|7f?fpMdtFrb<
z{broa0upys+iN%E*eh(EdTxWou|ocz-zTrRbdax8?(}<Y9Zl=6=l5<F-1L3J3r1z1
zYcm^O7x79x>=Az*64<oS>Ym@r_0KP^?m2UKo7<dfbKO<BioX|}Hf`fA^G~yU+|1PQ
zMpuI8T5Q7iQYjVFn7#iGO2)Rtl*&rXS#js|i}>S`ir&v^^IzOMmg~RG{^;{(f~QLK
zo_JOn?)Vj$EOD1LboO)EEtjuomOQ&38`%BS=H+|C72ke%T(Vid;MOgbWezbM;%9mb
z4(t4~dKoCuIorsPHR+<s8qLo~L^SHB{F%6SYK8VAuRWsG*}9cye>K10KNGb4q1DzW
zngz|<{dR=jJ6YTIONyyiUsvyJuX>v7z4F)M=huDt%cN~JnF|!&sC_zcD1)LvK|#UD
z5<X03jM@1G^|4)2i<65o3rg~fAl=*iyb`~}+*Ad9cQ+@O2ybn_%-p2X;-LK8#5~=g
z)b!GvM1(@O#N5oBN(Bvw8U?T-O^7i$iRs0#9&>(P33Pr**U-#DLD$H_P{Gi^05r#C
zY7Cuc@+?Wr$xL?4OV3GFFaR6jSe%@iSE68MVGQPi+zI0A8XKB}1)LKLJW?~$GfET;
z4NM_wf=g0!!xSta`av8I7zgB2x6GVWV+C;67Cg=dn-~C%6@Y>ZG^+;cxGLy_RD<n6
z?a+dSoDz#uLGpwH2sCKmoRL_hU~B}|>62Jo0_GbUL5CIc^GZP8f&{+;ID#M@Y}dTx
z{FKbRbOrtJ%sj`u;!KzT*r4#tl#+~Mg=hsMQ&5JYE;cp>ji;cRX=Vl*4?q<|=9!p)
z!VsA>H2}#QnS%-k0|gLmZf>Cf5rvQ-dyFkC!EzwAAPkZLPdh5;hvbLmWrAj%6~F}v
za)cSf#+*PA1|75kI~o#pxCSR6Dh(BkEDTIgMkcO?WS4|o6}|Vo?)e#&nP;AyGvGXb
zMDp-cSs@{2wFP_<Q`&>#oRWHZ4UTjqG->oNGYny2xtMS<P;jEsQmG5eL=+WoB=Oow
zU0TI5EiBsAakcNqKv(MrebpD%t-HGQ*8W)A=ku!1{rmR#P5%92eoZB>Wm8!;J=fi9
z>SCTICKxHGbabkzxlUBg#Y?O%Q7N}d4<8bpdOB{uVeqwRm;H;g{>{k<JF9(k(R-ns
zl&K8&j^F9-^r@ftJ6v~HX{Eu6cOsQdC%zqeRax9ou>ZtTC3f+%k#UQ~cME;vcICTz
z$7p}rmfyjVvv`eGomk}6_tI;#^QPk9`5vq6yw`2kI(a2}R?%&%-EI@^-n@Eq>h;6&
z->ehscLZJDsrsV&oyhS!`_|j-K59Bc#8q{_>#n9hQ)E3~J#>u<%JMq!F30-%wQFWg
zN}ieXwytDfD>nJ|*UIp^d6NyJmZryB6gVujkCE`>|J{7;_h0d8q3`F~&0T-_q|I-S
zd(*mh&JA0z^XKdD?<NP89#_52^?6Rp>qXtlnJlb}6E%(U9v9u7>;A{K+s$K_`ybcJ
zi4SbHo>&!ldTmv9Yvik<`#xV&rmp^!A{xf3mGk!5>%dQ6kH3$Ye%$=^<@DP=QGbj&
zYdX?j?v6?P6lgCc>iJr<Aiej!;D?le{VFjNGv~iPH9c#NkBG{n*O!wfU5+;TqkE6{
z+UA+tHoUS4S8*-+bF<D`=F{yw-OsHjG$w4-<oT(8itp#uF0rdCzP$<CYq5IsnqM2Z
z3g_*5scdIG@2}p9={x56yRUz$U(qn@%M`7!S|h2@C%$!_qCv)6z3cm=GP`eS1}&{Q
zaI`6B^S29GyL=}+58WM={*+_eWV?lnlXgzKb#aBK?;<A0&U*%8wd>L@#dQWQX<BvS
z?WHBlU+k^gm3K}41)tQ?=`Z+V7fxTnlw-d6jGv^dMGotW)Ljj;uHN3#!uP;g<iP^H
zi*{AgvKdQ)H+4_@@%D;?^@^|}&Q)2fwr8z<*|aCaDr57Ptc&F<*1lSiQtq&JQSujo
zEvAjzRwW-=J@?!NtutF*J$)k<F?G`aZlTrAf6Oln`97QBrMRt)Yn%DU_zQPFzxR1E
zBl-Dn^-rDInQCtfOm{cE%eko<xN+{Q%BxRrx!iuCvF>ovo|R#*bN;r>bKt!n#vpn{
zVWYWvP0ZA+)&l=8w_HlHXRZtA{jzXf!TG5-+J$>k&hNcek{II2o~l!P^HAoNsNT{^
znNG7kW#4&Ph5u1)+U*x19J+Xd*ojrs<}I_G(kx->vE*}2?BX+$AMY&k=XlOm+F#mc
z72wpoGHCv^sNe}2Zd>lZ{q=1FKle@FX~u@PL}rFbRjt&SWBlg+kqK}4OfOzhd*2mM
zT>kw^(B11(OlQ{l7EGG8WpeE!drki*JhN@Knq2wv^~a?5i~81U2<Eu0)DfO^ps8Qq
za=mxXtrVF`wJ?*`XQ8dvZol5#ef{?5?&2q>gpOVNde*sYxy%p8TQl@uG^u!P*?uiY
z>fiaFryoCG_i3u?e$}K&f68C&Y20(SJK~+Ke0`;j-P!POvj5gEd)gBADqJ&b-P^v|
z`$}F|?{PWC$2noj4*m1hnP-+P3~^m4baz>Ms`#asVQpu2-HeiaX?MDV{Ubkn{L{y$
zCC>f$!1}oO*nQcWXNQ*?);xOf_-pdn<2{!R|LC@@v-l@<+`Wgt`{VS&9}OSt?EL1=
zN%T8f5X9qu?m+eXXS2RPsxTK<mw0b*@7(eE%|C*9@(u6tJm@d2SS-5UxUc)?M=P1v
zdoIbWc78t9;#X9B@sy8I@q12Hw0>ki_FhufP$u)dk-Nm($RDwGacO%t+{%x8(SBGm
zBiZKs58cO>#}tp{OYBdxIc;$wBUR?Z;?&;cD2cPbqkWB&|L-f>ykGQp_^aCU7HRR7
zOQe4*{gPy_mfYW!$p3hHkJ>SP34iyGQ}}n6Tc(wZ?3Q9qo8EkkVcwJ_^Lrk19y>2-
zEosl4!2bB-Tf5H{cH4e`xU8|Q^W-)Ox#XN$ldCzYHnX~P`@fh)FRDn{oGbUT_pF(m
z-$Cad_T;$F3d+xpGC%s_!1F!-)6C!OiIe&5J0I`sUHi=L*s->v%^O9f!(X*k%U%xX
zYwOr|{h)0RZ#loYv_v`o@v4P8>vXQ&eQNl+X~*g2txRirlX^q4dYiA--8mUi+J1jc
z(w&FL`z5s{zxH^1e_LAmtjsM|wob(L?U|C`*ALozM0=jv>3AQ#By#824%0r>!aG98
zA6aBcT<w`H$$fZ7=f(r}=X7Q?N=t^8?r?1JI#%O0#jxLSy5VvO(ZZPdT}8*fOI|lR
z<rVA`DYH~_#@vgy&zw81bIf$pXVb?9#<Ip!a?`#X`l7JR_f_ID!(~+;Y>!P@oon1$
zxV3k+#AH|FnTDB*a@D>bIO4N@W=3+8c(~EJj>H-s)t=L9Wr{0h9!D9L87cLgmY5zV
zWH6nr@Z=1WVo!!-x9YPqJj$iqssqnxB*oZhW$5)KU-7uz!<Ce>@OaObz!wKyBQ-uK
z)wdjfV(eBiVft&s%D5+01~%$9dA3iS+>`iI!s>{j^I{1ji-a}{37G>68v7(o#F%Ay
z3T)CGq-6Mi8E=vlU#6&IbC|JZ(GG<^orM!bU6+afUDEVdqW19%W4^tvFV4OYb@g8v
z;_udGk^05WO8LZ#gB%@>4G+cF{VUw?dV*MM|3lxi261kyB9^BeIP9@;;u#O2%_?oy
z9N{8SQ=<GFtXNo2ug#LyW<SMd7_zx*-9C5Tzx5ek_WM29zwJyu!{kcF9xQEUP@@Ob
z2n4m64UEk|DnMLgP{RhqKyGV*=1g$6HBfpn0lTw~7zn)iDjFTv<-AQMNYZ(SiQXp#
zKRbtMVRnu>om*pmyx%;npF72|>E=zzwu#gKE#<ds{<9#1?aYIk4K3a=Clz`uekx?K
zUYlLx{M3B2pVOv_8`FA<<zqy0xj#)lsd|}hdAhWFjR1qf{gX;R4GzBiZ6vcg(f1{L
zI*+8*#nOa}8}F|6%dc{q;9B!e_p@Do`n12XHMyLQqA~IleYWgS$(>L#BVdcDKl|Fp
zFIm`r_viCneQ_o<c;~vGyRyzChfhda67scV!LowIT7Kqd-|ZAH;LizDIu{kCrTD$V
z?!n#@BA3@`y%%5bxl9%mWM~}`P(XnK4-}}z@W~}(*xC<Jm?9e7h?X$8kqc^LLpma!
zk)9Ebq1rB~S&3n#!HIdraCun&10tmWk|WUlFfcMu&^0kLQZO{PG*&P)GBzUA|FAT&
z0NV$09=QKuWNZo+K<a-OL0kBsE(iYphmiuf^@`G*1+}d~p@bS7U_0Rb4`)voP=J6!
z3(}cDbVINQkF%#saAk2xYOZHqT0Y1ukm*6G>6yhPMU@H~jw$&`so<~zO`7@_rKA>t
zx*HmvDXDoSnI)BQso>Irf}GS`kk7&0D(I?4kYhk00_(bfq7;%P!WE(o6rvT(3=H%P
zEX~bK%@oWGjPwjl4a_YJK?|?+EKN*}4UH7cj4kvGEsRYqO%!5dLG5v9cMLq8ODH%%
z;Q)4yKA~`cb(|FRVP4bq00oCW$n~jtDT#R{AiscmQ^uf(2m<#%kh&k>5&$K>Kz$mR
z10kIX1!K@)2gLulx*zbU1i2k;ZZtV1Au%Z-B}Ifw&-0A8r;Zorx--6~&TH~<q$Q*z
zCL|=VBpsK(#ABZ#QGdel?}YS!iU&X4{``Gi{Pnu68&5H*&i~YWf}Kg>Q?EkD6=tCx
zPAB`6N{PDgPX_OwBqk=Lrlef`(5G#3$=HB{mn)p(oWHiFzmC_{z=Cu7D|AlzoYx36
zFfuR+^;i|ca7uU~%d;5P71g3lO&d8FV-K%M$Y%J|Cey6I%&n}<y*uXJ_wJhdn4fiP
z{wnH9eM-N$P`>*{efvg-$eR6o_kaIiBJ@}9=Zo!s-ha72Q*D20-RXbR4FBo<w*7qX
z%jVO5C++W+R9$y|d9LK*i7zt$i+;}9q2_I?c{DTabJCMV;%hW-DgLdveER*)`^7==
zlBYlaefN4=V(IHN>ocVjejoRnIRD$C*VVs%{r*)|Rb5pb{^>)`>?`*#Z%)X%e`H?g
zUz<G)FLqB<#8M7{Vh0psphXJC@I?wHpe`p!7?d@j5orP%B*7h#sAc=Xyu%7Sdq0cX
zZENo`*}KRixcp>d^wu1ChXYGIxE0!EK7BV{@@k3fhs}TgtZ9F`wf=4Md4+tDvkj7S
z_@@<gYD=~Vs>>hQ$@<#2F2r<Jq`G3HO^)}mo&0)SOC9QrcBb5V@FD4OhdU#~r)Hf=
z{K7K()*rqnb!|#r!LbPo1!LL8WY<?;ei?h7V^f#^-qd@~-yYetzjM8=;+Cy;@2A0w
z_7%%sI#^!k<oPCFep7U@ak;P4*3?az5-q!K%rY+6_g(T--|>>0Vf+4W$qZ8}i^vaN
zD;jL~;B$@UvPG-ji>I0vpTG=Ga2SEY4P30lmr9!;cgsPE95Rjq%4d*L0-WtYnGI5`
zM+JpCg+^)zmn7z;Bo?IvSLP<==M)D7!<E5GcbEzVs1k*MU~usSTAPl2kjcV8LDvXW
zz8hGA2AK>E2o>_?=IDjI5u}(!D&!3eAtessLf%-x7*s|e7aHINDWEU|r8Pw0fc=VE
zGJu5;r5gTF!a2lbhINDq97T}SjVKo>9AN^D*?=+<Hf(BQ2?=@R@f>irLkSyD<$)SD
zn5%M3Ky3+#)BO}6qkWK7IndESY{f2eZuRXq%sXtr<61udQT|pz2c<}BN9M!cn?z!p
z6rwLX7O=QyBuY*)`toh-)GaR#J)GSCBsn0^e(}s~-i6CDqF-G8p0bcXZNo-}1^4f$
zK9XfRBq(or>*wtm2VAeGJ`(uz^xEx)P3C$P8y@vWE#9-t<mlRKma<JV*RAV6)xL1m
zyX+>@ljm=|{vlayJU>;{tKgsV-NhRnp8ucn`SCrK?xOvoLWv8-AMKj>wd+UcieI&F
z^)?%ytof<<IFe`24IO8DV>Z`+SaKmKKtQ1eTDfD1$c31J84;A422NGbGS1Kp(tyDh
zWT4hSaAsAif(c}hHC!RuP{ByS2vREs<>!|un1GtZkeC3qEfh>ZO=oa?LR)_ob41VE
z@-YUAus--4C-9$ZQN?7ziwS>vI*)NhG-T*HC|z9bvhc!X?>Eg}OSdt09%3`;DW0XT
z{(at~IEKQUhYZ~^31=oOSn{M>+cVGem9J6hq`MQEE-rEsihmRyYT0S)X@A7^>BNi)
zf1G?g3)CLY5;>hx5W>|lyHoXJ+#~la^Gjb^{Ib^`>D$7;#8~Yv|I3%p{<)m_+S4p}
p&87U@BJ~gKTKgmmF$1)?B(bQZq9`?u%h1T&+=xq6)z#mP3jlRMJuUzM
literal 0
HcmV?d00001
diff --git a/src/qmc-loop-algorithm-report.tex b/src/qmc-loop-algorithm-report.tex
index 7e93fce..aeea767 100644
--- a/src/qmc-loop-algorithm-report.tex
+++ b/src/qmc-loop-algorithm-report.tex
@@ -1,6 +1,7 @@
\ifx\pdfminorversion\undefined\else\pdfminorversion=4\fi
-\documentclass[aspectratio=169,t]{beamer}
-\usepackage[institute=Nat,aspectratio=169]{styles/beamerthemefau}
+\documentclass{beamer}
+\usepackage[institute=Nat]{styles/beamerthemefau}
+\usefonttheme{professionalfonts}
\usepackage[UKenglish]{babel}
\usepackage[utf8]{inputenc}
@@ -19,30 +20,165 @@
\date{2022-12-12}
\title{Quantum Monte Carlo and the Loop Algorithm}
+\subtitle{Physics Seminar}
\author{Stefan Gehr}
+\institute[FAU]{Friedrich-Alexander Universität Erlangen-Nürnberg}
\begin{document}
-\begin{frame}
- \titlepage
-\end{frame}
+\begin{trueplainframe}
+\titlepage
+\end{trueplainframe}
+
\begin{frame}{Table of contents}
\tableofcontents
\end{frame}
-\section{Monte Carlo Basics}
-\begin{frame}{Monte Carlo Basics}
-\begin{minipage}{0.40\linewidth}
-\begin{align*}
- a^2 + b^2 = c^2
-\end{align*}
+\section{Classic Monte Carlo}
+\begin{frame}{Metropolis Algorithm}
+\begin{minipage}{0.45\linewidth}
+ Classic Ising model
+ \begin{align*}
+ H(\vec{\sigma}) &= - \sum_{i}\left(J\sigma_i\sigma_{i+1} + \mu \sigma_i\right) \\
+ \sigma_i &\in \{-1, +1\}\qquad \vec{\sigma} = (\sigma_1, \dots, \sigma_N) \\
+ Z &= \sum_{\vec{\sigma}} w_{\vec{\sigma}} = \sum_{\vec{\sigma}}e^{-\beta H(\vec{\sigma})}
+ \end{align*}
+ We want to create a Markov chain of configurations \((\vec{\sigma}_1, \vec{\sigma}_2, \dots)\) where
+ \(N_{\vec{\sigma}_i} \propto e^{-\beta E(\vec{\sigma}_i)}\) \\
+ Detailed Balance condition
+ \begin{align*}
+ w_{\vec{\sigma}_i}\, p(\vec{\sigma}_i \to \vec{\sigma}_j)
+ = w_{\vec{\sigma}_j}\, p(\vec{\sigma}_j \to \vec{\sigma}_i)
+ \end{align*}
+ assures configuration \(\vec{\sigma}_i\) is sampled with correct weight \(w_{\vec{\sigma}_i}\).
+\end{minipage}
+\hfill
+\begin{minipage}{0.45\linewidth}
+ Metropolis:
+ \begin{align*}
+ p(\vec{\sigma}_i \to \sigma_j) = p_{\text{prop}}(\vec{\sigma}_i \to \sigma_j)p_{\text{acc}}(\vec{\sigma}_i \to \sigma_j) \\
+ \Rightarrow \frac{p_{\text{acc}}(\vec{\sigma}_i\to \vec{\sigma}_j)}{p_{\text{acc}}(\vec{\sigma}_j\to \vec{\sigma}_i)}
+ = \frac{p_{\text{prop}}(\vec{\sigma}_j\to \vec{\sigma}_i)w_{\vec{\sigma}_j}}{p_{\text{prop}}(\vec{\sigma}_i\to \vec{\sigma}_j)w_{\vec{\sigma}_i}}
+ \end{align*}
+ Choose e.g. \(p_{\text{prop}}(\vec{\sigma}_i\to \vec{\sigma}_j) = \frac{1}{N}\) (flip one of \(N\) sites)
+ Accept the new configuration \(\vec{\sigma}_j\) with probability
+ \begin{align*}
+ \min\left(1,\frac{p_{\text{acc}}(\vec{\sigma}_i\to \vec{\sigma}_j)}{p_{\text{acc}}(\vec{\sigma}_j\to \vec{\sigma}_i)}\right)
+ = \min\left(1,e^{-\beta\, [H(\vec{\sigma}_j) - H(\vec{\sigma}_i)]}\right)
+ .\end{align*}
+\end{minipage}
+\end{frame}
+\begin{frame}{Example with Numbers}
+ \(N = 4, J = 1, \mu = 2, \beta = 1\) \\
+ Start with random configuration \(\vec{\sigma}_0 = (\uparrow, \uparrow, \downarrow, \uparrow) = (1, 1, -1, 1)\).
+ Markov chain \(M = (\vec{\sigma}_0) = ((\uparrow, \uparrow, \downarrow, \uparrow))\).
+ \begin{align*}
+ H((\uparrow, \uparrow, \downarrow, \uparrow))
+ = -1\left(\uparrow \uparrow + \uparrow \downarrow + \downarrow \uparrow + \uparrow \uparrow\right) -2 \left(\uparrow + \uparrow + \downarrow + \uparrow\right) = -2\times 2 = -4
+ .\end{align*}
+ Suggest to flip first site \(\vec{\sigma}_1 \overset{?}{=} (\downarrow,\uparrow,\downarrow,\uparrow)\)
+ \begin{align*}
+ H((\downarrow, \uparrow, \downarrow, \uparrow))
+ = -1\left(\downarrow \uparrow + \uparrow \downarrow + \downarrow \uparrow + \uparrow \downarrow\right) -2 \left(\downarrow + \uparrow + \downarrow + \uparrow\right) = -1 \times (-4) = 4
+ .\end{align*}
+ Accept with probability
+ \begin{align*}
+ \min\left(1, e^{-1 \left[4 - (-4)\right]}\right) = e^{-8} \approx \num{0.000335} \\
+ \text{random number }r = \num{0.2} > \num{0.000335} \Rightarrow \text{decline} \Rightarrow \vec{\sigma}_1 = \vec{\sigma}_0 = (\uparrow, \uparrow, \downarrow, \uparrow) \\
+ M = (\vec{\sigma}_0, \vec{\sigma}_1) = ((\uparrow, \uparrow, \downarrow, \uparrow), (\uparrow, \uparrow, \downarrow, \uparrow))
+ .\end{align*}
+ Suggest to flip third site \(\vec{\sigma}_2 \overset{?}{=} (\uparrow, \uparrow, \uparrow, \uparrow)\)
+ \begin{align*}
+ H((\uparrow, \uparrow, \uparrow, \uparrow))
+ = -1\left(\uparrow \uparrow + \uparrow \uparrow + \uparrow \uparrow + \uparrow \uparrow\right) -2 \left(\uparrow + \uparrow + \uparrow + \uparrow\right) = -1 \times 4 - 2 \times 4 = -12 \\
+ \min\left(1, e^{-1 \left[-12 - (-4)\right]}\right) = \min(1, e^{16}) = 1 \ge r \Rightarrow \text{accept} \\
+ \Rightarrow M = (\vec{\sigma}_0, \vec{\sigma}_1, \vec{\sigma}_2) = ((\uparrow, \uparrow, \downarrow, \uparrow), (\uparrow, \uparrow, \downarrow, \uparrow), (\uparrow, \uparrow, \uparrow, \uparrow))
+ .\end{align*}
+\end{frame}
+\begin{frame}{Heat-Bath Algorithm}
+ Sample the proposed change with correct probability \(\Rightarrow\) change gets always accepted. \\
+ The local energy of site \(i\) is
+ \begin{align*}
+ E_i(\sigma_i) = -J \left(\sigma_{i-1}\sigma_i + \sigma_i\sigma_{i+1}\right) -\mu\sigma_i
+ .\end{align*}
+ The possible values are \(\sigma_i \in \{\uparrow, \downarrow\} = \{+1,-1\}\). We set site \(i\) to \(\uparrow\) with probability
+ \begin{align*}
+ p(\uparrow) = \frac{e^{-\beta E_i(\uparrow)}}{e^{-\beta E_i(\uparrow)} + e^{-\beta E_i(\downarrow)}}
+ .\end{align*}
+ \(N = 4, J = 1, \mu = 2, \beta = 1\) \\
+ Start with random configuration \(\vec{\sigma}_0 = (\uparrow, \uparrow, \downarrow, \uparrow) = (1, 1, -1, 1)\). \(M = ((\uparrow, \uparrow, \downarrow, \uparrow))\) \\
+ Set value at site 1
+ \begin{align*}
+ E_1(\uparrow) &= -1\left(\uparrow\uparrow + \uparrow\uparrow\right) - 2\uparrow = -1 \times 2 - 2 \times 1 = -4 \\
+ E_1(\downarrow) &= -1\left(\uparrow\downarrow + \downarrow\uparrow\right) - 2\downarrow = -1 \times (-2) - 2 \times (-1) = 4 \\
+ p(\uparrow) &= \frac{e^{-1 \times (-4)}}{e^{-1\times (-4)} + e^{-1 \times 4}} \approx \num{0.99966} \\
+ \text{random number }r &= 0.84 < \num{0.99966} \Rightarrow \sigma_1 = \downarrow \,\Rightarrow \vec{\sigma}_1 = (\uparrow, \uparrow, \downarrow, \uparrow) \\
+ M &= ((\uparrow, \uparrow, \downarrow, \uparrow), (\uparrow, \uparrow, \downarrow, \uparrow))
+ .\end{align*}
+\end{frame}
+\begin{frame}{Observables}
+\begin{itemize}
+ \item We start saving the Markov chain after a certain amount of sweeps (equilibrium was reached).
+ \item Easily calculate expectation values \(\expval{O} = \frac{1}{Z}\sum_{\vec{\sigma}}w_{\vec{\sigma}}O(\vec{\sigma}) \approx \frac{1}{\abs{M}}\sum_{i=1}^{\abs{M}}O(\vec{\sigma}_i)\)
+ \item For uncertainties use blocking analysis
+\end{itemize}
+\end{frame}
+\section{Quantum Monte Carlo}
+\begin{frame}{Quantum Monte Carlo}
+\begin{minipage}{0.45\linewidth}
+ XXZ quantum spin chain
+ \begin{align*}
+ H &= J_x \sum_i (S_i^xS_{i+1}^x + S_i^yS_{i+1}^y) + J_z\sum_i S_i^z S_{i+1}^z \\
+ &= \frac{J_x}{2}\sum_i \left(S_i^+S_{i+1}^- + S_i^-S_{i+1}^+\right) + J_z \sum_i S_i^z S_{i+1}^z \\
+ &\text{with}\quad S^+ = S^x + iS^y, \quad S^- = S^x - iS^y
+ .\end{align*}
+ Look at two sites only
+ \begin{align*}
+ H_{\text{two sites}} = \frac{J_x}{2}(S_1^+S_2^-+S_1^-S_2^+)+J_zS_1^zS_2^z \\
+ H_{\text{two sites}} \frac{1}{\sqrt{2}}(\ket{\uparrow\downarrow}\pm\ket{\downarrow\uparrow})
+ = \left(-\frac{J_z}{4}\pm\frac{J_x}{2}\right)\frac{1}{\sqrt{2}}(\ket{\uparrow\downarrow}\pm\ket{\downarrow\uparrow}) \\
+ H_{\text{two sites}} \ket{\uparrow\uparrow}
+ = \frac{J_z}{4}\ket{\uparrow\uparrow} \qquad
+ H_{\text{two sites}} \ket{\downarrow\downarrow}
+ = \frac{J_z}{4}\ket{\downarrow\downarrow}
+ .\end{align*}
\end{minipage}
\hfill
-\begin{minipage}{0.55\linewidth}
-\begin{align*}
- \sqrt{a} + \sqrt{b} \ne \sqrt{c}
-\end{align*}
+\begin{minipage}{0.45\linewidth}
+ \begin{align*}
+ \vcenter{\hbox{\includegraphics{square.none.pdf}}} &\equiv \bra{\downarrow\downarrow} e^{-\Delta\tau H_{\text{two sites}}} \ket{\downarrow\downarrow} = e^{\Delta\tau J_z / 4}\\
+ \vcenter{\hbox{\includegraphics{square.left.right.pdf}}} &\equiv \bra{\uparrow\uparrow} e^{-\Delta\tau H_{\text{two sites}}} \ket{\uparrow\uparrow} = e^{\Delta\tau J_z / 4} \\
+ \vcenter{\hbox{\includegraphics{square.left.pdf}}} &\equiv \bra{\uparrow\downarrow} e^{-\Delta\tau H_{\text{two sites}}} \ket{\uparrow\downarrow} = e^{\Delta\tau J_z /4}\cosh(\Delta\tau J_x /2) \\
+ \vcenter{\hbox{\includegraphics{square.right.pdf}}} &\equiv \bra{\downarrow\uparrow} e^{-\Delta\tau H_{\text{two sites}}} \ket{\downarrow\uparrow} = e^{\Delta\tau J_z /4}\cosh(\Delta\tau J_x /2) \\
+ \vcenter{\hbox{\includegraphics{square.diag.rl.pdf}}} &\equiv \bra{\uparrow\downarrow} e^{-\Delta\tau H_{\text{two sites}}} \ket{\downarrow\uparrow} = -e^{\Delta\tau J_z /4}\sinh(\Delta\tau J_x /2) \\
+ \vcenter{\hbox{\includegraphics{square.diag.lr.pdf}}} &\equiv \bra{\downarrow\uparrow} e^{-\Delta\tau H_{\text{two sites}}} \ket{\uparrow\downarrow} = -e^{\Delta\tau J_z /4}\sinh(\Delta\tau J_x /2)
+ \end{align*}
\end{minipage}
\end{frame}
+\begin{frame}{Quantum Monte Carlo}
+\begin{minipage}{0.45\linewidth}
+ Trotter decomposition
+ \begin{align*}
+ H &= \underbrace{\frac{J_x}{2}\sum_{\text{odd } i}(S_i^+S_{i+1}^-+S_i^-S_{i+1}^+) + J_z\sum_{\text{odd } i}S_i^zS_{i+1}^z}_{H_1} \\
+ &+ \underbrace{\frac{J_x}{2}\sum_{\text{even }i}(S_i^+S_{i+1}^-+S_i^-S_{i+1}^+) + J_z\sum_{\text{even }i}S_i^zS_{i+1}^z}_{H_2}
+ .\end{align*}
+ \begin{align*}
+ \tr\left[e^{-\beta H}\right]
+ &= \tr\left[\left(e^{-\Delta\tau H}\right)^m\right] \\
+ &= \tr\left[\left(e^{-\frac{\Delta\tau}{2}H_2}e^{-\Delta\tau H_1}e^{-\frac{\Delta\tau}{2}H_2} + \mathcal{O}(\Delta\tau^3)\right)^m\right] \\
+ &= \tr\left[\left(e^{-\Delta\tau H_1}e^{-\Delta\tau H_2}\right)^m\right] + \mathcal{O}(\Delta\tau^2) \\
+ &= \sum_{\vec{\sigma}_1\cdots\vec{\sigma}_{2m}}\bra{\vec{\sigma}_1}e^{-\Delta\tau H_1}\ketbra{\vec{\sigma}_{2m}}
+ e^{-\Delta\tau H_2}\ket{\vec{\sigma}_{2m-1}} \\
+ &\cdots\bra{\vec{\sigma}_3}e^{-\Delta\tau H_1}\ketbra{\vec{\sigma}_{2}}
+ e^{-\Delta\tau H_2}\ket{\vec{\sigma}_{1}}
+ + \mathcal{O}(\Delta\tau^2)
+ .\end{align*}
+\end{minipage}
+\hfill
+\begin{minipage}{0.45\linewidth}
+ \includegraphics[width=0.8\linewidth]{worldline.pdf}
+\end{minipage}
+\end{frame}
+
{
\nocite{*}
\printbibliography
diff --git a/src/references.bib b/src/references.bib
index 046271b..327c7c2 100644
--- a/src/references.bib
+++ b/src/references.bib
@@ -16,3 +16,31 @@
note = {Personal note}
}
+@unpublished{werner,
+ author = {Philipp Werner},
+ title = {Continuous-Time Impurity Solvers (Lecture Notes)},
+ institution = {Autumn-School Hands-on LDA=DMFT},
+ year = {2011},
+ url = {https://www.cond-mat.de/events/correl11/manuscript/Werner.pdf},
+ note = {Class handout}
+}
+
+@incollection{Assaad,
+ doi = {10.1007/978-3-540-74686-7_10},
+ url = {https://doi.org/10.1007/978-3-540-74686-7_10},
+ publisher = {Springer Berlin Heidelberg},
+ pages = {277--356},
+ author = {F.F. Assaad and H.G. Evertz},
+ title = {World-line and Determinantal Quantum Monte Carlo Methods for Spins, Phonons and Electrons},
+ booktitle = {Computational Many-Particle Physics}
+}
+
+@inproceedings{Sandvik2010,
+ doi = {10.1063/1.3518900},
+ url = {https://doi.org/10.1063/1.3518900},
+ year = {2010},
+ publisher = {{AIP}},
+ author = {Anders W. Sandvik and Adolfo Avella and Ferdinando Mancini},
+ title = {Computational Studies of Quantum Spin Systems},
+ booktitle = {{AIP} Conference Proceedings}
+}
--
GitLab