这里使用julia并行计算Wilson loop。
前言
这里还是使用BHZ模型为例来做计算，其实主要也就是稍微将代码进行了一些改动，使得其能进行并行计算，提高计算效率。
代码
using DelimitedFiles
using ProgressMeter
@everywhere using SharedArrays, LinearAlgebra,Distributed,DelimitedFiles
@everywhere function pauli()
hn::Int64 = 2
g0 = zeros(ComplexF64,hn,hn)
gx = zeros(ComplexF64,hn,hn)
gy = zeros(ComplexF64,hn,hn)
gz = zeros(ComplexF64,hn,hn)
#---------------
g0[1,1] = 1
g0[2,2] = 1
gx[1,2] = 1
gx[2,1] = 1
gy[1,2] = -im
gy[2,1] = im
gz[1,1] = 1
gz[2,2] = -1
return g0,gx,gy,gz
end
#---------------------------------------------------------------
@everywhere function hamset(kx::Float64,ky::Float64,m0::Float64)::Matrix{ComplexF64}
# m0::Float64 = 1.5
tx::Float64 = 1.
ty::Float64 = 1.
ax::Float64 = 1.
ay::Float64 = 1.
s0,sx,sy,sz = pauli()
ham = (m0 - tx*cos(kx) - ty*cos(ky))*kron(s0,sz) + ax*sin(kx)*kron(sz,sx) + ay*sin(ky)*kron(s0,sy)
return ham
end
#--------------------------------------------------------------------------------------
@everywhere function Wilson_kx(kx::Float64,m0::Float64)
nky::Int64 = 100
hn::Int64 = 4
Nocc::Int64 = Int(hn/2)
wave = zeros(ComplexF64,hn,hn,nky) # 存储哈密顿量对应的波函数
wan = zeros(ComplexF64,Nocc,Nocc) # 存储Wannier哈密顿量对应的波函数
F = zeros(ComplexF64,Nocc,Nocc)
vec2 = zeros(ComplexF64,Nocc,Nocc) # 重新排列顺序后Wannier Hamiltonian的本征矢量
kylist = range(0, 2*pi, length = nky)
for iy in 1:nky # 固定kx，沿着ky方向计算Wilson loop
ky = kylist[iy]
val,vec = eigen(hamset(kx,ky,m0))
wave[:,:,iy] = vec[:,:] # 存储波函数
end
wave[:,:,nky] = wave[:,:,1] # 在边界上波函数首尾相接
for i1 in 1:Nocc
F[i1,i1] = 1 # 构建单位矩阵
end
for i1 in 1:nky - 1 # index ki lattice
for i2 in 1:Nocc
for i3 in 1:Nocc
wan[i2,i3] = wave[:,i2,i1]' * wave[:,i3,i1 + 1] # 计算Berry联络
end
end
F = wan * F # 沿着ky方向构造Wannier哈密顿量
end
val,vec = eigen(F) # 对求解得到的本征矢量按照本征值大小排列
val = map(angle,val)
for i0 in 1:length(val)
if val[i0] < 0
val[i0] += 1
end
end
return val
end
#-------------------------------------------------------------------------------------
@everywhere function Wilson_ky(ky::Float64,m0::Float64)
nkx::Int64 = 100
hn::Int64 = 4
Nocc::Int64 = Int(hn/2)
wave = zeros(ComplexF64,hn,hn,nkx)
wan = zeros(ComplexF64,Nocc,Nocc)
F = zeros(ComplexF64,Nocc,Nocc)
vec2 = zeros(ComplexF64,Nocc,Nocc) # 重新排列顺序后Wannier Hamiltonian的本征矢量
kxlist = range(0, 2*pi, length = nkx)
for ix in 1:nkx # 固定ky，沿着kx方向计算Wilson loop
kx = kxlist[ix]
val,vec = eigen(hamset(kx,ky,m0))
wave[:,:,ix] = vec[:,:]
end
wave[:,:,nkx] = wave[:,:,1] # 波函数首尾相接
for i1 in 1:Nocc
F[i1,i1] = 1
end
for i1 in 1:nkx - 1
for i2 in 1:Nocc
for i3 in 1:Nocc
wan[i2,i3] = wave[:,i2,i1]' * wave[:,i3,i1 + 1] # 计算Berry联络
end
end
F = wan * F # 构造Wannier 哈密顿量
end
val,vec = eigen(F) # 对求解得到的本征矢量按照本征值大小排列
val = map(angle,val)
for i0 in 1:length(val)
if val[i0] < 0
val[i0] += 1
end
end
return val
end
#-----------------------------------------------------------------------------------------------
@everywhere function Wilsonloop(m0::Float64,cont::Int64)
# 改变质量看Wilson loop变化
klist = -pi:0.1:pi
re1 = zeros(Float64,length(klist),2)
re2 = zeros(Float64,length(klist),2)
i0 = 0
for kx in klist
i0 += 1
x1 = Wilson_kx(kx,m0)
x2 = Wilson_ky(kx,m0)
re1[i0,:] = x1
re2[i0,:] = x2
end
fx1 = "Wilson-kx-" * string(cont) * ".dat"
f1 = open(fx1,"w")
writedlm(f1,[klist re1],"\t")
close(f1)
fx1 = "Wilson-ky-" * string(cont) * ".dat"
f1 = open(fx1,"w")
writedlm(f1,[klist re2],"\t")
close(f1)
end
#------------------------------------------------------------------------------
function main()
i0 = 1
for m0 in -1:0.1:1
Wilsonloop(m0,i0)
i0 += 1
end
end
#-----------------------------------------------------------------------------------------------
@time Wilsonloop(1.5,1)
# @time main()
公众号
相关内容均会在公众号进行同步，若对该Blog感兴趣，欢迎关注微信公众号。
