A package to enable block respecting compression of Matrix Product Operators (MPOs) for use with ITensors.jl.
Reference: Daniel E. Parker, Xiangyu Cao, and Michael P. Zaletel Phys. Rev. B 102, 035147
ITensors has built in support for generating MPOs from local operators. This framework is called AutoMPO. MPOs
generated by AutoMPO are already compressed, so you only need this package
if you:
1. Are using MPOs that are created by hand, outside the `AutoMPO` framework.
2. Want your MPO to be in orthogonal/canonical form.
3. Need to see the bond spectrums throughout the lattice.
Support for compression of infinite lattice MPOs (iMPOs) is in the ITensorInfiniteMPS package which can be found here.
Technical notes on what this package does can be founs here
You can install this package through the Julia package manager:
julia> ] add ITensorMPOCompressionHere are is an example of orthogonalizing an hand generated (not using AutoMPO) MPO
julia> using ITensors
julia> using ITensorMPOCompression
julia> include("../test/hamiltonians/hamiltonians.jl");
julia> N = 10; #10 sites
julia> NNN = 7; #Include up to 7th nearest neighbour interactions
julia> sites = siteinds("S=1/2", N);
julia> H = transIsing_MPO(sites, NNN);
julia> is_regular_form(H,lower) == true
true
julia> @show get_Dw(H); #Show bond dimensions
get_Dw(H) = [30, 30, 30, 30, 30, 30, 30, 30, 30]
julia> pprint(H[2]) #schematic view of operators at site #2
I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0 0 0
S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 I 0 0
0 S 0 S 0 0 S 0 0 0 S 0 0 0 0 S 0 0 0 0 0 S 0 0 0 0 0 0 S I
julia> orthogonalize!(H,left); #Orthogonalize into left canonical form. Also does rank reduction.
julia> orthogonalize!(H,right); #Orthogonalize into right canoncial form.
julia> pprint(H[2]) #Show vastly reduced matrix of operators at site #2
I 0 0 0
S S S 0
0 S 0 I
julia> @show get_Dw(H); #Show reduced bond dimensions
get_Dw(H) = [3, 4, 5, 6, 7, 6, 5, 4, 3]
julia> is_regular_form(H,lower) == true
true
julia> isortho(H, right) == true #looks at cached ortho center limits
true
julia> check_ortho(H,right) == true #Does the more expensive V*V_dagger==Id contraction and test
true
julia> pprint(H) #High level view of what is in the MPO.
n Dw1 Dw2 d Reg. Orth.
Form Form
1 1 3 2 L M
2 3 4 2 L R
3 4 5 2 L R
4 5 6 2 L R
5 6 7 2 L R
6 7 6 2 L R
7 6 5 2 L R
8 5 4 2 L R
9 4 3 2 L R
10 3 1 2 L BHere are is an example of truncating an hand generated (not using AutoMPO) MPO
julia> using ITensors
julia> using ITensorMPOCompression
julia> include("../test/hamiltonians/hamiltonians.jl");
julia> N = 10; #10 sites
julia> NNN = 7; #Include up to 7th nearest neighbour interactions
julia> sites = siteinds("S=1/2", N);
julia> H = transIsing_MPO(sites, NNN);
julia> is_regular_form(H,lower) == true
true
julia> spectrums = truncate!(H,left);
julia> pprint(H[5])
I 0 0 0 0 0 0
S S S S S S 0
S S S S S S 0
S S S S S S 0
S S S S S S 0
0 S S S S S I
julia> @show get_Dw(H);
get_Dw(H) = [3, 4, 5, 6, 7, 6, 5, 4, 3]
julia> @show spectrums;
spectrums =
Bond Ns max(s) min(s) Entropy Tr. Error
1 1 0.30739 3.07e-01 0.22292 0.00e+00
2 2 0.35392 3.49e-02 0.26838 0.00e+00
3 3 0.37473 2.06e-02 0.29133 0.00e+00
4 4 0.38473 1.77e-02 0.30255 0.00e+00
5 5 0.38773 7.25e-04 0.30588 0.00e+00
6 4 0.38473 1.77e-02 0.30255 0.00e+00
7 3 0.37473 2.06e-02 0.29133 0.00e+00
8 2 0.35392 3.49e-02 0.26838 0.00e+00
9 1 0.30739 3.07e-01 0.22292 0.00e+00
julia> is_regular_form(H,lower) == true
true
julia> isortho(H, left) == true
true
julia> check_ortho(H, left) == true
trueThis file was generated with weave.jl with the following commands:
using ITensorMPOCompression, Weave
weave(
joinpath(pkgdir(ITensorMPOCompression), "examples", "README.jl");
doctype="github",
out_path=pkgdir(ITensorMPOCompression),
)