OutOfMemoryError in DMRG

DMRG and Numerical Methods
,
1

Hi, dear developers

Recently, I used Itensor (Julia) to calculate the ground state energy of the two-dimensional Hubbard model. This system has 27 sites, so the filled electrons can be set to 1, 2, …, 53. In addition, the total z-component spin is not a good quantum number due to the Rashba-SOC term in the Hamiltonian. Unfortunately, due to memory limitations on my computer cluster, I could only calculate up to 7 filled electrons. Please forgive me as I am a new user of julia and Itensor. Is there some way to optimize the memory and increase the maximum number of filled electrons?
Furthermore, the reference article (FIG. 16) claims that 48 sites with 24 filled electrons can be achieved.

My code is following:

using Distributed
addprocs(2)
@show nprocs()
@everywhere using Dates, DelimitedFiles, SharedArrays, ITensors, ITensorMPS


let
U = 0.5;
transNew = readdlm("transNew_27.txt");
N = length(union(transNew[:,1])); #number of sites: 27

####################################################################
nsweeps = 40;
maxdim = [20, 60, 80, 100, 200, 400, 600, 800, 1000, 2000, 3000, 6000, 8000, 10000, 20000, 30000, 50000, 100000];
cutoff = [1E-8];
noise = [1E-7, 1E-8, 1E-10, 0.];

####################################################################
sites = siteinds("Electron", N ; conserve_qns=true, conserve_sz=false);
lattice = Lattice(undef, size(transNew)[1]);
for i in range(start = 1 , step = 1 , stop = size(transNew)[1])
    lattice[i] = LatticeBond(convert(Int, transNew[i,1]), convert(Int, transNew[i,5]), transNew[i,2], transNew[i,3], transNew[i,6], transNew[i,7])
end

####################################################################
os = OpSum()
for (i,b) in enumerate(lattice)
    os -= transNew[i,9]+1im * transNew[i,10], (convert(Int, transNew[i,4]) == 0 ? "Cdagup" : "Cdagdn"), b.s1, (convert(Int, transNew[i,8]) == 0 ? "Cup" : "Cdn"), b.s2;
end
for n in 1:N
    os += U, "Nupdn", n;
end
H = MPO(os, sites);

@sync @distributed for indexx in range(start = 1 , step = 1 , stop = 53)
result = zeros(Float64, 2*N-1);
beginTime = Dates.Time(Dates.now());

Npart = indexx; #number of particles
p = Npart;
state = Vector{String}(undef, N);
for i in range(start=N, step=-1, stop=1)
	if p > i
		# println("Doubly occupying site ",i);
		state[i] = "UpDn";
		p -= 2;
	elseif p > 0
		# println("Singly occupying site ",i);
		state[i] = (isodd(i) ? "Up" : "Dn");
		p -= 1;
	else
		state[i] = "Emp";
	end
end

####################################################################
psi0 = random_mps(sites, state);
t1 = @elapsed begin
    energy, psi = dmrg(H, psi0; nsweeps, maxdim, cutoff, noise);
    end
result[indexx] = energy;
endTime = Dates.Time(Dates.now());
println("sites = $N, filled electons = $indexx, \t begin at $beginTime, \t end at $endTime, \t DMRG costs time: $t1");
writedlm("dataFile_$indexx.txt", result);
end
end

transNew_27.txt contains information about the lattice and hopping parameters (periodic boundary condition in x direction, open boundary condition in y condition) as shown below:

1	-0.5	-0.2886751345948129	0	12	2.	0.	0	1.	0.
1	-0.5	-0.2886751345948129	0	12	2.	0.	1	-0.17320508075688776	-0.10000000000000003
1	-0.5	-0.2886751345948129	0	10	0.	0.	0	1.	0.
1	-0.5	-0.2886751345948129	0	10	0.	0.	1	0.17320508075688776	-0.10000000000000003
1	-0.5	-0.2886751345948129	1	12	2.	0.	0	0.17320508075688776	-0.10000000000000003
1	-0.5	-0.2886751345948129	1	12	2.	0.	1	1.	0.
1	-0.5	-0.2886751345948129	1	10	0.	0.	0	-0.17320508075688776	-0.10000000000000003
1	-0.5	-0.2886751345948129	1	10	0.	0.	1	1.	0.
2	0.5	-0.2886751345948129	0	10	0.	0.	0	1.	0.
2	0.5	-0.2886751345948129	0	10	0.	0.	1	-0.17320508075688776	-0.10000000000000003
2	0.5	-0.2886751345948129	0	11	1.	0.	0	1.	0.
2	0.5	-0.2886751345948129	0	11	1.	0.	1	0.17320508075688776	-0.10000000000000003
2	0.5	-0.2886751345948129	1	10	0.	0.	0	0.17320508075688776	-0.10000000000000003
2	0.5	-0.2886751345948129	1	10	0.	0.	1	1.	0.
2	0.5	-0.2886751345948129	1	11	1.	0.	0	-0.17320508075688776	-0.10000000000000003
2	0.5	-0.2886751345948129	1	11	1.	0.	1	1.	0.
3	1.5	-0.2886751345948129	0	11	1.	0.	0	1.	0.
3	1.5	-0.2886751345948129	0	11	1.	0.	1	-0.17320508075688776	-0.10000000000000003
3	1.5	-0.2886751345948129	0	12	2.	0.	0	1.	0.
3	1.5	-0.2886751345948129	0	12	2.	0.	1	0.17320508075688776	-0.10000000000000003
3	1.5	-0.2886751345948129	1	11	1.	0.	0	0.17320508075688776	-0.10000000000000003
3	1.5	-0.2886751345948129	1	11	1.	0.	1	1.	0.
3	1.5	-0.2886751345948129	1	12	2.	0.	0	-0.17320508075688776	-0.10000000000000003
3	1.5	-0.2886751345948129	1	12	2.	0.	1	1.	0.
4	0.	0.5773502691896257	0	15	2.5	0.8660254037844386	0	1.	0.
4	0.	0.5773502691896257	0	15	2.5	0.8660254037844386	1	-0.17320508075688776	-0.1
4	0.	0.5773502691896257	0	10	0.	0.	0	1.	0.
4	0.	0.5773502691896257	0	10	0.	0.	1	0.	0.2
4	0.	0.5773502691896257	0	13	0.5	0.8660254037844386	0	1.	0.
4	0.	0.5773502691896257	0	13	0.5	0.8660254037844386	1	0.17320508075688776	-0.1
4	0.	0.5773502691896257	1	15	2.5	0.8660254037844386	0	0.17320508075688776	-0.1
4	0.	0.5773502691896257	1	15	2.5	0.8660254037844386	1	1.	0.
4	0.	0.5773502691896257	1	10	0.	0.	0	0.	0.2
4	0.	0.5773502691896257	1	10	0.	0.	1	1.	0.
4	0.	0.5773502691896257	1	13	0.5	0.8660254037844386	0	-0.17320508075688776	-0.1
4	0.	0.5773502691896257	1	13	0.5	0.8660254037844386	1	1.	0.
5	1.	0.5773502691896257	0	11	1.	0.	0	1.	0.
5	1.	0.5773502691896257	0	11	1.	0.	1	0.	0.2
5	1.	0.5773502691896257	0	13	0.5	0.8660254037844386	0	1.	0.
5	1.	0.5773502691896257	0	13	0.5	0.8660254037844386	1	-0.17320508075688776	-0.1
5	1.	0.5773502691896257	0	14	1.5	0.8660254037844386	0	1.	0.
5	1.	0.5773502691896257	0	14	1.5	0.8660254037844386	1	0.17320508075688776	-0.1
5	1.	0.5773502691896257	1	11	1.	0.	0	0.	0.2
5	1.	0.5773502691896257	1	11	1.	0.	1	1.	0.
5	1.	0.5773502691896257	1	13	0.5	0.8660254037844386	0	0.17320508075688776	-0.1
5	1.	0.5773502691896257	1	13	0.5	0.8660254037844386	1	1.	0.
5	1.	0.5773502691896257	1	14	1.5	0.8660254037844386	0	-0.17320508075688776	-0.1
5	1.	0.5773502691896257	1	14	1.5	0.8660254037844386	1	1.	0.
6	2.	0.5773502691896257	0	12	2.	0.	0	1.	0.
6	2.	0.5773502691896257	0	12	2.	0.	1	0.	0.2
6	2.	0.5773502691896257	0	14	1.5	0.8660254037844386	0	1.	0.
6	2.	0.5773502691896257	0	14	1.5	0.8660254037844386	1	-0.17320508075688776	-0.1
6	2.	0.5773502691896257	0	15	2.5	0.8660254037844386	0	1.	0.
6	2.	0.5773502691896257	0	15	2.5	0.8660254037844386	1	0.17320508075688776	-0.1
6	2.	0.5773502691896257	1	12	2.	0.	0	0.	0.2
6	2.	0.5773502691896257	1	12	2.	0.	1	1.	0.
6	2.	0.5773502691896257	1	14	1.5	0.8660254037844386	0	0.17320508075688776	-0.1
6	2.	0.5773502691896257	1	14	1.5	0.8660254037844386	1	1.	0.
6	2.	0.5773502691896257	1	15	2.5	0.8660254037844386	0	-0.17320508075688776	-0.1
6	2.	0.5773502691896257	1	15	2.5	0.8660254037844386	1	1.	0.
7	0.5	1.4433756729740643	0	18	3.	1.7320508075688772	0	1.	0.
7	0.5	1.4433756729740643	0	18	3.	1.7320508075688772	1	-0.17320508075688776	-0.1
7	0.5	1.4433756729740643	0	13	0.5	0.8660254037844386	0	1.	0.
7	0.5	1.4433756729740643	0	13	0.5	0.8660254037844386	1	0.	0.2
7	0.5	1.4433756729740643	0	16	1.	1.7320508075688772	0	1.	0.
7	0.5	1.4433756729740643	0	16	1.	1.7320508075688772	1	0.17320508075688776	-0.1
7	0.5	1.4433756729740643	1	18	3.	1.7320508075688772	0	0.17320508075688776	-0.1
7	0.5	1.4433756729740643	1	18	3.	1.7320508075688772	1	1.	0.
7	0.5	1.4433756729740643	1	13	0.5	0.8660254037844386	0	0.	0.2
7	0.5	1.4433756729740643	1	13	0.5	0.8660254037844386	1	1.	0.
7	0.5	1.4433756729740643	1	16	1.	1.7320508075688772	0	-0.17320508075688776	-0.1
7	0.5	1.4433756729740643	1	16	1.	1.7320508075688772	1	1.	0.
8	1.5	1.4433756729740643	0	14	1.5	0.8660254037844386	0	1.	0.
8	1.5	1.4433756729740643	0	14	1.5	0.8660254037844386	1	0.	0.2
8	1.5	1.4433756729740643	0	16	1.	1.7320508075688772	0	1.	0.
8	1.5	1.4433756729740643	0	16	1.	1.7320508075688772	1	-0.17320508075688776	-0.1
8	1.5	1.4433756729740643	0	17	2.	1.7320508075688772	0	1.	0.
8	1.5	1.4433756729740643	0	17	2.	1.7320508075688772	1	0.17320508075688776	-0.1
8	1.5	1.4433756729740643	1	14	1.5	0.8660254037844386	0	0.	0.2
8	1.5	1.4433756729740643	1	14	1.5	0.8660254037844386	1	1.	0.
8	1.5	1.4433756729740643	1	16	1.	1.7320508075688772	0	0.17320508075688776	-0.1
8	1.5	1.4433756729740643	1	16	1.	1.7320508075688772	1	1.	0.
8	1.5	1.4433756729740643	1	17	2.	1.7320508075688772	0	-0.17320508075688776	-0.1
8	1.5	1.4433756729740643	1	17	2.	1.7320508075688772	1	1.	0.
9	2.5	1.4433756729740643	0	15	2.5	0.8660254037844386	0	1.	0.
9	2.5	1.4433756729740643	0	15	2.5	0.8660254037844386	1	0.	0.2
9	2.5	1.4433756729740643	0	17	2.	1.7320508075688772	0	1.	0.
9	2.5	1.4433756729740643	0	17	2.	1.7320508075688772	1	-0.17320508075688776	-0.1
9	2.5	1.4433756729740643	0	18	3.	1.7320508075688772	0	1.	0.
9	2.5	1.4433756729740643	0	18	3.	1.7320508075688772	1	0.17320508075688776	-0.1
9	2.5	1.4433756729740643	1	15	2.5	0.8660254037844386	0	0.	0.2
9	2.5	1.4433756729740643	1	15	2.5	0.8660254037844386	1	1.	0.
9	2.5	1.4433756729740643	1	17	2.	1.7320508075688772	0	0.17320508075688776	-0.1
9	2.5	1.4433756729740643	1	17	2.	1.7320508075688772	1	1.	0.
9	2.5	1.4433756729740643	1	18	3.	1.7320508075688772	0	-0.17320508075688776	-0.1
9	2.5	1.4433756729740643	1	18	3.	1.7320508075688772	1	1.	0.
10	0.	0.	0	21	2.5	0.2886751345948129	0	1.	0.
10	0.	0.	0	21	2.5	0.2886751345948129	1	0.17320508075688776	0.10000000000000003
10	0.	0.	0	4	0.	0.5773502691896257	0	1.	0.
10	0.	0.	0	4	0.	0.5773502691896257	1	0.	-0.2
10	0.	0.	0	1	-0.5	-0.2886751345948129	0	1.	0.
10	0.	0.	0	1	-0.5	-0.2886751345948129	1	-0.17320508075688776	0.10000000000000003
10	0.	0.	0	2	0.5	-0.2886751345948129	0	1.	0.
10	0.	0.	0	2	0.5	-0.2886751345948129	1	0.17320508075688776	0.10000000000000003
10	0.	0.	0	19	0.5	0.2886751345948129	0	1.	0.
10	0.	0.	0	19	0.5	0.2886751345948129	1	-0.17320508075688776	0.10000000000000003
10	0.	0.	0	10	0.	0.	0	0.6	0.
10	0.	0.	1	21	2.5	0.2886751345948129	0	-0.17320508075688776	0.10000000000000003
10	0.	0.	1	21	2.5	0.2886751345948129	1	1.	0.
10	0.	0.	1	4	0.	0.5773502691896257	0	0.	-0.2
10	0.	0.	1	4	0.	0.5773502691896257	1	1.	0.
10	0.	0.	1	1	-0.5	-0.2886751345948129	0	0.17320508075688776	0.10000000000000003
10	0.	0.	1	1	-0.5	-0.2886751345948129	1	1.	0.
10	0.	0.	1	2	0.5	-0.2886751345948129	0	-0.17320508075688776	0.10000000000000003
10	0.	0.	1	2	0.5	-0.2886751345948129	1	1.	0.
10	0.	0.	1	19	0.5	0.2886751345948129	0	0.17320508075688776	0.10000000000000003
10	0.	0.	1	19	0.5	0.2886751345948129	1	1.	0.
10	0.	0.	1	10	0.	0.	1	0.6	0.
11	1.	0.	0	5	1.	0.5773502691896257	0	1.	0.
11	1.	0.	0	5	1.	0.5773502691896257	1	0.	-0.2
11	1.	0.	0	2	0.5	-0.2886751345948129	0	1.	0.
11	1.	0.	0	2	0.5	-0.2886751345948129	1	-0.17320508075688776	0.10000000000000003
11	1.	0.	0	3	1.5	-0.2886751345948129	0	1.	0.
11	1.	0.	0	3	1.5	-0.2886751345948129	1	0.17320508075688776	0.10000000000000003
11	1.	0.	0	19	0.5	0.2886751345948129	0	1.	0.
11	1.	0.	0	19	0.5	0.2886751345948129	1	0.17320508075688776	0.10000000000000003
11	1.	0.	0	20	1.5	0.2886751345948129	0	1.	0.
11	1.	0.	0	20	1.5	0.2886751345948129	1	-0.17320508075688776	0.10000000000000003
11	1.	0.	0	11	1.	0.	0	0.6	0.
11	1.	0.	1	5	1.	0.5773502691896257	0	0.	-0.2
11	1.	0.	1	5	1.	0.5773502691896257	1	1.	0.
11	1.	0.	1	2	0.5	-0.2886751345948129	0	0.17320508075688776	0.10000000000000003
11	1.	0.	1	2	0.5	-0.2886751345948129	1	1.	0.
11	1.	0.	1	3	1.5	-0.2886751345948129	0	-0.17320508075688776	0.10000000000000003
11	1.	0.	1	3	1.5	-0.2886751345948129	1	1.	0.
11	1.	0.	1	19	0.5	0.2886751345948129	0	-0.17320508075688776	0.10000000000000003
11	1.	0.	1	19	0.5	0.2886751345948129	1	1.	0.
11	1.	0.	1	20	1.5	0.2886751345948129	0	0.17320508075688776	0.10000000000000003
11	1.	0.	1	20	1.5	0.2886751345948129	1	1.	0.
11	1.	0.	1	11	1.	0.	1	0.6	0.
12	2.	0.	0	1	-0.5	-0.2886751345948129	0	1.	0.
12	2.	0.	0	1	-0.5	-0.2886751345948129	1	0.17320508075688776	0.10000000000000003
12	2.	0.	0	6	2.	0.5773502691896257	0	1.	0.
12	2.	0.	0	6	2.	0.5773502691896257	1	0.	-0.2
12	2.	0.	0	3	1.5	-0.2886751345948129	0	1.	0.
12	2.	0.	0	3	1.5	-0.2886751345948129	1	-0.17320508075688776	0.10000000000000003
12	2.	0.	0	20	1.5	0.2886751345948129	0	1.	0.
12	2.	0.	0	20	1.5	0.2886751345948129	1	0.17320508075688776	0.10000000000000003
12	2.	0.	0	21	2.5	0.2886751345948129	0	1.	0.
12	2.	0.	0	21	2.5	0.2886751345948129	1	-0.17320508075688776	0.10000000000000003
12	2.	0.	0	12	2.	0.	0	0.6	0.
12	2.	0.	1	1	-0.5	-0.2886751345948129	0	-0.17320508075688776	0.10000000000000003
12	2.	0.	1	1	-0.5	-0.2886751345948129	1	1.	0.
12	2.	0.	1	6	2.	0.5773502691896257	0	0.	-0.2
12	2.	0.	1	6	2.	0.5773502691896257	1	1.	0.
12	2.	0.	1	3	1.5	-0.2886751345948129	0	0.17320508075688776	0.10000000000000003
12	2.	0.	1	3	1.5	-0.2886751345948129	1	1.	0.
12	2.	0.	1	20	1.5	0.2886751345948129	0	-0.17320508075688776	0.10000000000000003
12	2.	0.	1	20	1.5	0.2886751345948129	1	1.	0.
12	2.	0.	1	21	2.5	0.2886751345948129	0	0.17320508075688776	0.10000000000000003
12	2.	0.	1	21	2.5	0.2886751345948129	1	1.	0.
12	2.	0.	1	12	2.	0.	1	0.6	0.
13	0.5	0.8660254037844386	0	24	3.	1.1547005383792515	0	1.	0.
13	0.5	0.8660254037844386	0	24	3.	1.1547005383792515	1	0.17320508075688776	0.1
13	0.5	0.8660254037844386	0	4	0.	0.5773502691896257	0	1.	0.
13	0.5	0.8660254037844386	0	4	0.	0.5773502691896257	1	-0.17320508075688776	0.1
13	0.5	0.8660254037844386	0	5	1.	0.5773502691896257	0	1.	0.
13	0.5	0.8660254037844386	0	5	1.	0.5773502691896257	1	0.17320508075688776	0.1
13	0.5	0.8660254037844386	0	7	0.5	1.4433756729740643	0	1.	0.
13	0.5	0.8660254037844386	0	7	0.5	1.4433756729740643	1	0.	-0.2
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13	0.5	0.8660254037844386	0	19	0.5	0.2886751345948129	1	0.	-0.2
13	0.5	0.8660254037844386	0	22	1.	1.1547005383792515	0	1.	0.
13	0.5	0.8660254037844386	0	22	1.	1.1547005383792515	1	-0.17320508075688776	0.1
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13	0.5	0.8660254037844386	1	24	3.	1.1547005383792515	0	-0.17320508075688776	0.1
13	0.5	0.8660254037844386	1	24	3.	1.1547005383792515	1	1.	0.
13	0.5	0.8660254037844386	1	4	0.	0.5773502691896257	0	0.17320508075688776	0.1
13	0.5	0.8660254037844386	1	4	0.	0.5773502691896257	1	1.	0.
13	0.5	0.8660254037844386	1	5	1.	0.5773502691896257	0	-0.17320508075688776	0.1
13	0.5	0.8660254037844386	1	5	1.	0.5773502691896257	1	1.	0.
13	0.5	0.8660254037844386	1	7	0.5	1.4433756729740643	0	0.	-0.2
13	0.5	0.8660254037844386	1	7	0.5	1.4433756729740643	1	1.	0.
13	0.5	0.8660254037844386	1	19	0.5	0.2886751345948129	0	0.	-0.2
13	0.5	0.8660254037844386	1	19	0.5	0.2886751345948129	1	1.	0.
13	0.5	0.8660254037844386	1	22	1.	1.1547005383792515	0	0.17320508075688776	0.1
13	0.5	0.8660254037844386	1	22	1.	1.1547005383792515	1	1.	0.
13	0.5	0.8660254037844386	1	13	0.5	0.8660254037844386	1	0.6	0.
14	1.5	0.8660254037844386	0	5	1.	0.5773502691896257	0	1.	0.
14	1.5	0.8660254037844386	0	5	1.	0.5773502691896257	1	-0.17320508075688776	0.1
14	1.5	0.8660254037844386	0	6	2.	0.5773502691896257	0	1.	0.
14	1.5	0.8660254037844386	0	6	2.	0.5773502691896257	1	0.17320508075688776	0.1
14	1.5	0.8660254037844386	0	8	1.5	1.4433756729740643	0	1.	0.
14	1.5	0.8660254037844386	0	8	1.5	1.4433756729740643	1	0.	-0.2
14	1.5	0.8660254037844386	0	20	1.5	0.2886751345948129	0	1.	0.
14	1.5	0.8660254037844386	0	20	1.5	0.2886751345948129	1	0.	-0.2
14	1.5	0.8660254037844386	0	22	1.	1.1547005383792515	0	1.	0.
14	1.5	0.8660254037844386	0	22	1.	1.1547005383792515	1	0.17320508075688776	0.1
14	1.5	0.8660254037844386	0	23	2.	1.1547005383792515	0	1.	0.
14	1.5	0.8660254037844386	0	23	2.	1.1547005383792515	1	-0.17320508075688776	0.1
14	1.5	0.8660254037844386	0	14	1.5	0.8660254037844386	0	0.6	0.
14	1.5	0.8660254037844386	1	5	1.	0.5773502691896257	0	0.17320508075688776	0.1
14	1.5	0.8660254037844386	1	5	1.	0.5773502691896257	1	1.	0.
14	1.5	0.8660254037844386	1	6	2.	0.5773502691896257	0	-0.17320508075688776	0.1
14	1.5	0.8660254037844386	1	6	2.	0.5773502691896257	1	1.	0.
14	1.5	0.8660254037844386	1	8	1.5	1.4433756729740643	0	0.	-0.2
14	1.5	0.8660254037844386	1	8	1.5	1.4433756729740643	1	1.	0.
14	1.5	0.8660254037844386	1	20	1.5	0.2886751345948129	0	0.	-0.2
14	1.5	0.8660254037844386	1	20	1.5	0.2886751345948129	1	1.	0.
14	1.5	0.8660254037844386	1	22	1.	1.1547005383792515	0	-0.17320508075688776	0.1
14	1.5	0.8660254037844386	1	22	1.	1.1547005383792515	1	1.	0.
14	1.5	0.8660254037844386	1	23	2.	1.1547005383792515	0	0.17320508075688776	0.1
14	1.5	0.8660254037844386	1	23	2.	1.1547005383792515	1	1.	0.
14	1.5	0.8660254037844386	1	14	1.5	0.8660254037844386	1	0.6	0.
15	2.5	0.8660254037844386	0	4	0.	0.5773502691896257	0	1.	0.
15	2.5	0.8660254037844386	0	4	0.	0.5773502691896257	1	0.17320508075688776	0.1
15	2.5	0.8660254037844386	0	6	2.	0.5773502691896257	0	1.	0.
15	2.5	0.8660254037844386	0	6	2.	0.5773502691896257	1	-0.17320508075688776	0.1
15	2.5	0.8660254037844386	0	9	2.5	1.4433756729740643	0	1.	0.
15	2.5	0.8660254037844386	0	9	2.5	1.4433756729740643	1	0.	-0.2
15	2.5	0.8660254037844386	0	21	2.5	0.2886751345948129	0	1.	0.
15	2.5	0.8660254037844386	0	21	2.5	0.2886751345948129	1	0.	-0.2
15	2.5	0.8660254037844386	0	23	2.	1.1547005383792515	0	1.	0.
15	2.5	0.8660254037844386	0	23	2.	1.1547005383792515	1	0.17320508075688776	0.1
15	2.5	0.8660254037844386	0	24	3.	1.1547005383792515	0	1.	0.
15	2.5	0.8660254037844386	0	24	3.	1.1547005383792515	1	-0.17320508075688776	0.1
15	2.5	0.8660254037844386	0	15	2.5	0.8660254037844386	0	0.6	0.
15	2.5	0.8660254037844386	1	4	0.	0.5773502691896257	0	-0.17320508075688776	0.1
15	2.5	0.8660254037844386	1	4	0.	0.5773502691896257	1	1.	0.
15	2.5	0.8660254037844386	1	6	2.	0.5773502691896257	0	0.17320508075688776	0.1
15	2.5	0.8660254037844386	1	6	2.	0.5773502691896257	1	1.	0.
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15	2.5	0.8660254037844386	1	9	2.5	1.4433756729740643	1	1.	0.
15	2.5	0.8660254037844386	1	21	2.5	0.2886751345948129	0	0.	-0.2
15	2.5	0.8660254037844386	1	21	2.5	0.2886751345948129	1	1.	0.
15	2.5	0.8660254037844386	1	23	2.	1.1547005383792515	0	-0.17320508075688776	0.1
15	2.5	0.8660254037844386	1	23	2.	1.1547005383792515	1	1.	0.
15	2.5	0.8660254037844386	1	24	3.	1.1547005383792515	0	0.17320508075688776	0.1
15	2.5	0.8660254037844386	1	24	3.	1.1547005383792515	1	1.	0.
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16	1.	1.7320508075688772	0	27	3.5	2.0207259421636903	1	0.1732050807568877	0.10000000000000005
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16	1.	1.7320508075688772	0	7	0.5	1.4433756729740643	1	-0.17320508075688776	0.1
16	1.	1.7320508075688772	0	8	1.5	1.4433756729740643	0	1.	0.
16	1.	1.7320508075688772	0	8	1.5	1.4433756729740643	1	0.17320508075688776	0.1
16	1.	1.7320508075688772	0	22	1.	1.1547005383792515	0	1.	0.
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16	1.	1.7320508075688772	1	7	0.5	1.4433756729740643	1	1.	0.
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22	1.	1.1547005383792515	1	13	0.5	0.8660254037844386	1	1.	0.
22	1.	1.1547005383792515	1	14	1.5	0.8660254037844386	0	0.17320508075688776	-0.1
22	1.	1.1547005383792515	1	14	1.5	0.8660254037844386	1	1.	0.
22	1.	1.1547005383792515	1	16	1.	1.7320508075688772	0	0.	0.2
22	1.	1.1547005383792515	1	16	1.	1.7320508075688772	1	1.	0.
23	2.	1.1547005383792515	0	14	1.5	0.8660254037844386	0	1.	0.
23	2.	1.1547005383792515	0	14	1.5	0.8660254037844386	1	0.17320508075688776	-0.1
23	2.	1.1547005383792515	0	15	2.5	0.8660254037844386	0	1.	0.
23	2.	1.1547005383792515	0	15	2.5	0.8660254037844386	1	-0.17320508075688776	-0.1
23	2.	1.1547005383792515	0	17	2.	1.7320508075688772	0	1.	0.
23	2.	1.1547005383792515	0	17	2.	1.7320508075688772	1	0.	0.2
23	2.	1.1547005383792515	1	14	1.5	0.8660254037844386	0	-0.17320508075688776	-0.1
23	2.	1.1547005383792515	1	14	1.5	0.8660254037844386	1	1.	0.
23	2.	1.1547005383792515	1	15	2.5	0.8660254037844386	0	0.17320508075688776	-0.1
23	2.	1.1547005383792515	1	15	2.5	0.8660254037844386	1	1.	0.
23	2.	1.1547005383792515	1	17	2.	1.7320508075688772	0	0.	0.2
23	2.	1.1547005383792515	1	17	2.	1.7320508075688772	1	1.	0.
24	3.	1.1547005383792515	0	13	0.5	0.8660254037844386	0	1.	0.
24	3.	1.1547005383792515	0	13	0.5	0.8660254037844386	1	-0.17320508075688776	-0.1
24	3.	1.1547005383792515	0	15	2.5	0.8660254037844386	0	1.	0.
24	3.	1.1547005383792515	0	15	2.5	0.8660254037844386	1	0.17320508075688776	-0.1
24	3.	1.1547005383792515	0	18	3.	1.7320508075688772	0	1.	0.
24	3.	1.1547005383792515	0	18	3.	1.7320508075688772	1	0.	0.2
24	3.	1.1547005383792515	1	13	0.5	0.8660254037844386	0	0.17320508075688776	-0.1
24	3.	1.1547005383792515	1	13	0.5	0.8660254037844386	1	1.	0.
24	3.	1.1547005383792515	1	15	2.5	0.8660254037844386	0	-0.17320508075688776	-0.1
24	3.	1.1547005383792515	1	15	2.5	0.8660254037844386	1	1.	0.
24	3.	1.1547005383792515	1	18	3.	1.7320508075688772	0	0.	0.2
24	3.	1.1547005383792515	1	18	3.	1.7320508075688772	1	1.	0.
25	1.5	2.0207259421636903	0	16	1.	1.7320508075688772	0	1.	0.
25	1.5	2.0207259421636903	0	16	1.	1.7320508075688772	1	0.1732050807568877	-0.10000000000000005
25	1.5	2.0207259421636903	0	17	2.	1.7320508075688772	0	1.	0.
25	1.5	2.0207259421636903	0	17	2.	1.7320508075688772	1	-0.1732050807568877	-0.10000000000000005
25	1.5	2.0207259421636903	1	16	1.	1.7320508075688772	0	-0.1732050807568877	-0.10000000000000005
25	1.5	2.0207259421636903	1	16	1.	1.7320508075688772	1	1.	0.
25	1.5	2.0207259421636903	1	17	2.	1.7320508075688772	0	0.1732050807568877	-0.10000000000000005
25	1.5	2.0207259421636903	1	17	2.	1.7320508075688772	1	1.	0.
26	2.5	2.0207259421636903	0	17	2.	1.7320508075688772	0	1.	0.
26	2.5	2.0207259421636903	0	17	2.	1.7320508075688772	1	0.1732050807568877	-0.10000000000000005
26	2.5	2.0207259421636903	0	18	3.	1.7320508075688772	0	1.	0.
26	2.5	2.0207259421636903	0	18	3.	1.7320508075688772	1	-0.1732050807568877	-0.10000000000000005
26	2.5	2.0207259421636903	1	17	2.	1.7320508075688772	0	-0.1732050807568877	-0.10000000000000005
26	2.5	2.0207259421636903	1	17	2.	1.7320508075688772	1	1.	0.
26	2.5	2.0207259421636903	1	18	3.	1.7320508075688772	0	0.1732050807568877	-0.10000000000000005
26	2.5	2.0207259421636903	1	18	3.	1.7320508075688772	1	1.	0.
27	3.5	2.0207259421636903	0	16	1.	1.7320508075688772	0	1.	0.
27	3.5	2.0207259421636903	0	16	1.	1.7320508075688772	1	-0.1732050807568877	-0.10000000000000005
27	3.5	2.0207259421636903	0	18	3.	1.7320508075688772	0	1.	0.
27	3.5	2.0207259421636903	0	18	3.	1.7320508075688772	1	0.1732050807568877	-0.10000000000000005
27	3.5	2.0207259421636903	1	16	1.	1.7320508075688772	0	0.1732050807568877	-0.10000000000000005
27	3.5	2.0207259421636903	1	16	1.	1.7320508075688772	1	1.	0.
27	3.5	2.0207259421636903	1	18	3.	1.7320508075688772	0	-0.1732050807568877	-0.10000000000000005
27	3.5	2.0207259421636903	1	18	3.	1.7320508075688772	1	1.	0.

Notice: For safety reasons, we should not load too many CPU cores, and limit the number of filled electrons in the beginning.

@sync @distributed for indexx in range(start = 1 , step = 1 , stop = 3)

Thank you for your patience, I would be very grateful for any suggestions. I am looking to to hearing from you.

Regards,
Y.D.Shen.

2

Some thoughts:

  • See this page: High-Performance Computing FAQs · ITensors.jl
  • Do you actually need a max dim of 100,000? That seems quite high, especially as the paper you linked had a maxdim of 1,000
    • Also I recommend converging the lower bond dimensions, i.e. doing multiple sweeps before raising the maxdim
  • If you have access to enough disk space while running, you can have DMRG output the tensors that are not currently being optimized to disk with the keyword arguments to dmrg: write_when_maxdim_exceeds and write_path . See the docs for dmrg
    • This is slow, so it sacrifices time for less memory required
    • This may be complicated using with @distributed
  • Does the code crash when not using distributed for the hardest problem?
3

Thank you very much for your reply.

  • After reviewing your first suggestion, I realized that using distributed for loops might lead to excessive memory accumulation that wasn’t released promptly. To address this, I added GC.gc() at the start of each distributed for loop. Additionally, when running Julia, I appended julia --heap-size-hint=180G.
  • Regarding your suggestion to perform multiple sweeps before increasing maxdim, should it be set as follows?
    maxdim = [10, 10, 20, 20, 60, 80, 100, 100, 200, 200, 400, 500, 500, 600, 800, 1000];
    I’m uncertain why the same maxdim values are repeated in many tutorials. Furthermore, when I set maxdim = 1000 and subsequently observe maxlinkdim = 1000 after all sweeps, does this imply that maxdim = 1000 might not be sufficient?
  • The code does not crash when not using distributed.

I have three more questions.

  1. We set cutoff and nsweeps in DMRG. If the cutoff is reached before all sweeps are completed, can the program be terminated early?
  2. And, what the meaning of maxerr in the DMRG output?
  3. Finally, how can we determine whether our result reaches the cutoff, or if it’s possible that the cutoff isn’t reached due to too few nsweeps?

Thank you for your patience. I am looking to to hearing from you.

Regards,
Y.D.Shen.

4

A quick heuristic answer to this - if you can decrease the energy at a smaller maxdim, it’ll be faster than a larger maxdim. Also e.g. observables may need some time to stabilize due to the linear sweeping, for doing say cutoff extrapolation.

  1. Check out the checkdone! method here Observer System for DMRG · ITensors.jl
    You would need to determine the criteria for stopping early (for example, checking that the cutoff is reached and/or the energy has stopped decreasing)
  2. maxerr is the maximum truncation error during a dmrg sweep. The truncation error is the sum of the squares of the “thrown away” singular values during the truncation step inside of dmrg
  3. As with 1, you’ll have to set some criteria for considering a calculation to be “converged.” You can always try to extrapolate observables as a function of the cutoff as well
5

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