Dear ITensor
I am working on a frustrated antifermagnetic XX model on the 2d honeycomb lattice with nearest- and next-nearest neighbour interaction. Using ITensor, I was able to study lattice up to N=60 sites, but going to a bigger lattice size, N=90, I got a “core dumped” message on my pc with 96GB ram. I asked a friend to run the code with 500GB accessible memory, but again we received a “core dumped” error. There are 370 bound links( total of nn + nnn). Does the program need such a big ram, or I have done something wrong. The attached code is working correctly for lattice size N=60, and the changes for bigger system size related to the variables “bnd1” and “bnd1”. Any help would be appreciated.
Regards
Javad
P.S: the code attached below:
using namespace std;
using namespace itensor;
int
main()
{
auto N = 90;
//
// Initialize the site degrees of freedom.
//
auto sites = SpinHalf(N,{"ConserveQNs=",true});
// Set the initial wavefunction matrix product state
// to be a Neel state.
//
// This choice implicitly sets the global Sz quantum number
// of the wavefunction to zero. Since it is an MPS
// it will remain in this quantum number sector.
//
auto state = InitState(sites);
for(int i = 1; i <= N; ++i)
{
if(i%2 == 1)
state.set(i,"Up");
else
state.set(i,"Dn");
}
auto psi0 = MPS(state);
auto bnd1 = {1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 11,
12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 21, 22,
23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 31, 32, 33,
33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 41, 42, 43, 43,
44, 45, 45, 46, 47, 47, 48, 49, 49, 51, 52, 53, 53, 54,
55, 55, 56, 57, 57, 58, 59, 59, 61, 62, 63, 63, 64, 65,
65, 66, 67, 67, 68, 69, 69, 71, 72, 73, 73, 74, 75, 75,
76, 77, 77, 78, 79, 79, 81, 82, 83, 84, 85, 86, 87, 88,
89, 10, 20, 20, 30, 30, 40, 40, 50, 50, 60, 60, 70, 70,
80, 80, 90, 90,
1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7,
8, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14,
14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19,
20, 20, 21, 21, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25,
26, 26, 26, 27, 27, 27, 28, 28, 28, 29, 29, 30, 30, 31, 31,
32, 32, 33, 33, 33, 34, 34, 34, 35, 35, 35, 36, 36, 36, 37,
37, 37, 38, 38, 38, 39, 39, 40, 40, 41, 41, 42, 42, 43, 43,
43, 44, 44, 44, 45, 45, 45, 46, 46, 46, 47, 47, 47, 48, 48,
48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 53, 54, 54, 54,
55, 55, 55, 56, 56, 56, 57, 57, 57, 58, 58, 58, 59, 59, 60,
60, 61, 61, 62, 62, 63, 63, 63, 64, 64, 64, 65, 65, 65, 66,
66, 66, 67, 67, 67, 68, 68, 68, 69, 69, 70, 70, 71, 71, 72,
72, 73, 73, 73, 74, 74, 74, 75, 75, 75, 76, 76, 76, 77, 77,
77, 78, 78, 78, 79, 79, 80, 80, 81, 82, 83, 84, 85, 86, 87,
88, 10, 20, 20, 30, 30, 40, 40, 50, 50, 60, 60, 70, 70, 80,
80, 90, 90, 1, 1, 11, 11, 21, 21, 31, 31, 41, 41, 51, 51, 61,
61, 71, 71, 81};
auto bnd2 = {2, 3, 4, 12, 5, 6, 14, 7, 8, 16, 9, 10, 18, 12, 13,
14, 22, 15, 16, 24, 17, 18, 26, 19, 20, 28, 22, 23, 24, 32, 25,
26, 34, 27, 28, 36, 29, 30, 38, 32, 33, 34, 42, 35, 36, 44, 37,
38, 46, 39, 40, 48, 42, 43, 44, 52, 45, 46, 54, 47, 48, 56, 49,
50, 58, 52, 53, 54, 62, 55, 56, 64, 57, 58, 66, 59, 60, 68, 62,
63, 64, 72, 65, 66, 74, 67, 68, 76, 69, 70, 78, 72, 73, 74, 82,
75, 76, 84, 77, 78, 86, 79, 80, 88, 82, 83, 84, 85, 86, 87, 88,
89, 90, 1, 1, 11, 11, 21, 21, 31, 31, 41, 41, 51, 51, 61, 61, 71,
71, 81, 3, 11, 4, 12, 5, 11, 13, 6, 12, 14, 7, 13, 15, 8, 14, 16,
9, 15, 17, 10, 16, 18, 17, 19, 18, 20, 13, 21, 14, 22, 15, 21, 23,
16, 22, 24, 17, 23, 25, 18, 24, 26, 19, 25, 27, 20, 26, 28, 27, 29,
28, 30, 23, 31, 24, 32, 25, 31, 33, 26, 32, 34, 27, 33, 35, 28, 34,
36, 29, 35, 37, 30, 36, 38, 37, 39, 38, 40, 33, 41, 34, 42, 35, 41,
43, 36, 42, 44, 37, 43, 45, 38, 44, 46, 39, 45, 47, 40, 46, 48, 47,
49, 48, 50, 43, 51, 44, 52, 45, 51, 53, 46, 52, 54, 47, 53, 55, 48,
54, 56, 49, 55, 57, 50, 56, 58, 57, 59, 58, 60, 53, 61, 54, 62, 55,
61, 63, 56, 62, 64, 57, 63, 65, 58, 64, 66, 59, 65, 67, 60, 66, 68,
67, 69, 68, 70, 63, 71, 64, 72, 65, 71, 73, 66, 72, 74, 67, 73, 75,
68, 74, 76, 69, 75, 77, 70, 76, 78, 77, 79, 78, 80, 73, 81, 74, 82,
75, 81, 83, 76, 82, 84, 77, 83, 85, 78, 84, 86, 79, 85, 87, 80, 86,
88, 87, 89, 88, 90, 83, 84, 85, 86, 87, 88, 89, 90, 2, 2, 12, 12, 22,
22, 32, 32, 42, 42, 52, 52, 62, 62, 72, 72, 82, 9, 19, 19, 29, 29, 39,
49, 49, 59, 59, 69, 69, 79, 79, 89, 89};
auto Jb=0.0;
int n1=130;
std::ofstream enf("dmrg_45_46_47_svn_new.txt");
enf << "Jb, E0, Sz45, Sz46, Sz47, Sz45Sz46, Sz45Sz47, Sp45Sn46, Sp45Sn47, Svn, SvN_norm\n" << std::flush;
for (int jj=0; jj<=20; ++jj)
{
auto ampo = AutoMPO(sites);
int cte=0;
for(auto bnd : zip(bnd1,bnd2)){
auto [s1,s2] = bnd;
//printfln(" s1 : %i , s2 : %i ",bnd.s1,bnd.s2);
if (cte < n1)
{
//printfln(" cte : %i, s1 : %i , s2 : %i ",cte, s1,s2);
ampo += 0.5,"S+",s1,"S-",s2;
ampo += 0.5,"S-",s1,"S+",s2;
}
else
{
Jb=jj*0.02;
ampo += 0.5*Jb,"S+",s1,"S-",s2;
ampo += 0.5*Jb,"S-",s1,"S+",s2;
}
cte +=1;
}
auto H = toMPO(ampo);
//
// overlap calculates matrix elements of MPO's with respect to MPS's
// inner(psi0,H,psi0) = <psi0|H|psi0>
//
printfln("Initial energy = %.5f", inner(psi0,H,psi0) );
//
// Set the parameters controlling the accuracy of the DMRG
// calculation for each DMRG sweep.
// Here less than 5 cutoff values are provided, for example,
// so all remaining sweeps will use the last one given (= 1E-10).
//
auto sweeps = Sweeps(7);
sweeps.maxdim() = 10,20,200,400,600,800,1000;
sweeps.cutoff() = 1E-12;
sweeps.niter() = 2;
sweeps.noise() = 1E-7,1E-8,0.0;
//println(sweeps);
//
// Begin the DMRG calculation
// for the ground state
//
auto [en,psi] = dmrg(H,psi0,sweeps,{"Quiet=",true});
auto psi0 = psi;
//
// Measuring Sz
//
//println("==============================");
//println("======= Measuring Sz ==========");
//auto Sz = Vector(3);
float Sz [3] = {};
int cte0 = 0;
for( auto m : {45,46,47} )
{
//re-gauge psi to get ready to measure at position j
psi.position(m);
auto ket = psi(m);
auto bra = dag(prime(ket,"Site"));
auto szop = op(sites,"Sz",m);
//take an inner product
Sz[cte0] = elt(bra*szop*ket);
//printfln("%d %.12f %.12f",j,szj,sxj);
cte0+=1;
}
println("==============================");
println("======= SziSzj ==========");
int i = 45;
int cte1 = 0;
//auto SziSzj = Vector(2);
float SziSzj [2] = {};
for(auto j : {46,47})
{
auto Szi = op(sites,"Sz",i);
auto Szj = op(sites,"Sz",j);
psi.position(i);
auto C = psi(i);
C *=Szi;
auto ir = commonIndex(psi(i),psi(i+1),"Link");
C *= dag(prime(prime(psi(i),"Site"),ir));
for (int k=i+1; k<j; ++k)
{
C *= psi(k);
C *= dag(prime(psi(k),"Link"));
}
C *= psi(j);
C *= Szj;
auto il = commonIndex(psi(j),psi(j-1),"Link");
C *= dag(prime(prime(psi(j),"Site"),il));
SziSzj[cte1]=elt(C);
//printfln("\n Jb : %.4f, SzSz : %.10f",Jb, elt(C));
cte1+=1;
}
println("==============================");
println("======= SpiSnj ==========");
//auto SpiSnj=Vector(2);
float SpiSnj [2] = {};
int n = 45;
int cte2 = 0;
for(auto j : {46,47})
{
auto Spi = op(sites,"S+",n);
auto Snj = op(sites,"S-",j);
psi.position(n);
auto C = psi(n);
C *=Spi;
auto ir = commonIndex(psi(n),psi(n+1),"Link");
C *= dag(prime(prime(psi(n),"Site"),ir));
for (int k=n+1; k<j; ++k)
{
C *= psi(k);
C *= dag(prime(psi(k),"Link"));
}
C *= psi(j);
C *= Snj;
auto il = commonIndex(psi(j),psi(j-1),"Link");
C *= dag(prime(prime(psi(j),"Site"),il));
SpiSnj[cte2]=elt(C);
//printfln("\n Jb : %.4f, S+S- : %.10f",Jb, elt(C));
cte2+=1;
}
//compute EE
auto b = 45;
psi.position(b);
ITensor wf = psi.A(b)*psi.A(b+1);
auto U = psi.A(b);
ITensor S,V;
auto spectrum = svd(wf,U,S,V);
Real SvN = 0.;
for(auto p : spectrum.eigs())
{
if(p > 1E-12) SvN += -p*log(p);
}
auto normSvN = SvN /log(2);
printfln("\n Jb : %.4f, E0 : %.10f, Sz1 : %.10f, Sz2 : %.10f , Sz3 : %.10f, Sz1Sz2 : %.10f, Sz1Sz3 : %.10f, Sp1Sn2 : %.10f, Sp1Sn3 : %.10f, SvN : %.10f, normSvN : %.10f",
Jb, en, Sz[0], Sz[1], Sz[2], SziSzj[0], SziSzj[1], SpiSnj[0], SpiSnj[1], SvN, normSvN);
enf << format("%.4f %.10f %.10f %.10f %.10f %.10f %.10f %.10f %.10f %.10f %.10f\n",
Jb, en, Sz[0], Sz[1], Sz[2], SziSzj[0], SziSzj[1], SpiSnj[0], SpiSnj[1], SvN, normSvN)<< std::flush;
}
enf.close();
return 0;
}
and her is the lattice figure
