lattice/latticegpu.jl
1
0
Fork 0
mirror of https://igit.ific.uv.es/alramos/latticegpu.jl.git synced 2025-05-15 11:43:42 +02:00
Code Issues Projects Releases Packages Wiki Activity Actions

Working HMC for SU(2) and SU(3)

Browse source
This commit is contained in:
Alberto Ramos 2021-07-28 13:50:32 +02:00
parent f6be70070e
commit c378648508
6 changed files with 119 additions and 40 deletions
Download patch file Download diff file Expand all files Collapse all files

49
src/Groups/GroupSU3.jl
View file

@ -31,7 +31,7 @@ SU3() = SU3(1.0,0.0,0.0,0.0,1.0,0.0)
inverse(a::SU3) = SU3(conj(a.u11),conj(a.u21),(a.u12*a.u23 - a.u13*a.u22),
conj(a.u12),conj(a.u22),(a.u13*a.u21 - a.u11*a.u23))
dag(a::SU3) = inverse(a)
tr(g::SU3) = a.u11+a.u22+a.u11*conj(a.u22)-a.u12*conj(a.u21)
tr(a::SU3) = a.u11+a.u22+conj(a.u11*a.u22 - a.u12*a.u21)
function Base.:*(a::SU3,b::SU3)
@ -49,33 +49,33 @@ end
function Base.:/(a::SU3,b::SU3)
bu31 = conj(b.u12*a.u23 - b.u13*b.u22)
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
bu31 = (b.u12*b.u23 - b.u13*b.u22)
bu32 = (b.u13*b.u21 - b.u11*b.u23)
bu33 = (b.u11*b.u22 - b.u12*b.u21)
return SU3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
a.u11*conj(bu31) + a.u12*conj(bu32) + a.u13*conj(bu33),
a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
a.u21*conj(bu31) + a.u22*conj(bu32) + a.u23*conj(bu33))
a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33))
end
function Base.:\(a::SU3,b::SU3)
au31 = conj(a.u12*a.u23 - a.u13*a.u22)
au32 = conj(a.u13*a.u21 - a.u11*a.u23)
bu31 = conj(b.u12*a.u23 - b.u13*b.u22)
au31 = (a.u12*a.u23 - a.u13*a.u22)
au32 = (a.u13*a.u21 - a.u11*a.u23)
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
return SU3(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + conj(au31)*bu31,
conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + conj(au31)*bu32,
conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + conj(au31)*bu33,
conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + conj(au32)*bu31,
conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + conj(au32)*bu32,
conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + conj(au32)*bu33)
return SU3(conj(a.u11)*b.u11 + conj(a.u21)*b.u21 + (au31)*bu31,
conj(a.u11)*b.u12 + conj(a.u21)*b.u22 + (au31)*bu32,
conj(a.u11)*b.u13 + conj(a.u21)*b.u23 + (au31)*bu33,
conj(a.u12)*b.u11 + conj(a.u22)*b.u21 + (au32)*bu31,
conj(a.u12)*b.u12 + conj(a.u22)*b.u22 + (au32)*bu32,
conj(a.u12)*b.u13 + conj(a.u22)*b.u23 + (au32)*bu33)
end
@ -97,9 +97,7 @@ function projalg(a::SU3)
sr3ov2::Float64 = 0.866025403784438646763723170752
au33 = conj(a.u11*a.u22 - a.u12*a.u21)
ditr = ( imag(a.u11) + imag(a.u22) + imag(au33) )/3.0
ditr = ( imag(a.u11) + imag(a.u22) + 2.0*imag(a.u11*a.u22 - a.u12*a.u21) )/3.0
m12 = (a.u12 - conj(a.u21))/2.0
m13 = (a.u13 - (a.u12*a.u23 - a.u13*a.u22) )/2.0
m23 = (a.u23 - (a.u13*a.u21 - a.u11*a.u23) )/2.0
@ -107,8 +105,9 @@ function projalg(a::SU3)
return SU3alg(imag( m12 ), imag( m13 ), imag( m23 ),
real( m12 ), real( m13 ), real( m23 ),
(imag(a.u11)-imag(a.u22))/2.0,
-sr3ov2*(imag(au33)-ditr))
sr3ov2*(ditr))
end
dot(a::SU3alg,b::SU3alg) = a.t1*b.t1 + a.t2*b.t2 + a.t3*b.t3 + a.t4*b.t4 +
a.t5*b.t5 + a.t6*b.t6 + a.t7*b.t7 + a.t8*b.t8
norm2(a::SU3alg) = a.t1^2 + a.t2^2 + a.t3^2 + a.t4^2 + a.t5^2 + a.t6^2 + a.t7^2 + a.t8^2
@ -184,19 +183,19 @@ end
function Base.:/(a::M3x3,b::SU3)
bu31 = conj(b.u12*b.u23 - b.u13*b.u22)
bu32 = conj(b.u13*b.u21 - b.u11*b.u23)
bu33 = conj(b.u11*b.u22 - b.u12*b.u21)
bu31 = (b.u12*b.u23 - b.u13*b.u22)
bu32 = (b.u13*b.u21 - b.u11*b.u23)
bu33 = (b.u11*b.u22 - b.u12*b.u21)
return M3x3(a.u11*conj(b.u11) + a.u12*conj(b.u12) + a.u13*conj(b.u13),
a.u11*conj(b.u21) + a.u12*conj(b.u22) + a.u13*conj(b.u23),
a.u11*conj(bu31) + a.u12*conj(bu32) + a.u13*conj(bu33),
a.u11*(bu31) + a.u12*(bu32) + a.u13*(bu33),
a.u21*conj(b.u11) + a.u22*conj(b.u12) + a.u23*conj(b.u13),
a.u21*conj(b.u21) + a.u22*conj(b.u22) + a.u23*conj(b.u23),
a.u21*conj(bu31) + a.u22*conj(bu32) + a.u23*conj(bu33),
a.u21*(bu31) + a.u22*(bu32) + a.u23*(bu33),
a.u31*conj(b.u11) + a.u32*conj(b.u12) + a.u33*conj(b.u13),
a.u31*conj(b.u21) + a.u32*conj(b.u22) + a.u33*conj(b.u23),
a.u31*conj(bu31) + a.u32*conj(bu32) + a.u33*conj(bu33))
a.u31*(bu31) + a.u32*(bu32) + a.u33*(bu33))
end
Base.:*(a::Number,b::M3x3) = M3x3(a*b.u11, a*b.u12, a*bu13,