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View Code? Open in Web Editor NEWExact diagonalization, Lehmann's representation, Two-particle Green's functions
Home Page: http://pomerol-ed.github.io/pomerol/
License: Mozilla Public License 2.0
Exact diagonalization, Lehmann's representation, Two-particle Green's functions
Home Page: http://pomerol-ed.github.io/pomerol/
License: Mozilla Public License 2.0
Hi, we've found that it's very expensive to compute two-particle GF in Matsubara frequencies especially for a seven-orbital model.
The reason is obvious: pomerol first makes a list of terms by performing summation over all intermediate states, whose computational complexity may scale as O(N^4) (N is the dimension of the Hilbert space).
Instead, one could compute G(tau1, tau2, tau3, tau4) for a given (tau1, tau2, tau3, tau4), in which summation over intermediate states is no more necessary.
Is there any attempt to implement the computation of two-particle GF in imaginary time?
Dear Andrey and Igor,
I'm trying to use your tutorial example with the Hubbard dimer in ./tutorial/example2site.cpp. But I'm only getting zeros for the two-particle greens function, see below. What am I doing wrong?
Best regards, Hugo
Sites
Site "A", 1 orbital, 2 spins.
Site "B", 1 orbital, 2 spins.
Terms
-1*c^{+}_{A,0,0}c_{B,0,0}
-1*c^{+}_{B,0,0}c_{A,0,0}
-1*c^{+}_{A,0,1}c_{B,0,1}
-1*c^{+}_{B,0,1}c_{A,0,1}
-1*c^{+}_{A,0,0}c_{A,0,0}
-1*c^{+}_{A,0,1}c_{A,0,1}
-1*c^{+}_{B,0,0}c_{B,0,0}
-1*c^{+}_{B,0,1}c_{B,0,1}
Terms with 4 operators
2*c^{+}_{A,0,1}c_{A,0,1}c^{+}_{A,0,0}c_{A,0,0}
2*c^{+}_{B,0,1}c_{B,0,1}c^{+}_{B,0,0}c_{B,0,0}
=======
Indices
=======
Index 0 = (A,0,0)
Index 1 = (A,0,1)
Index 2 = (B,0,0)
Index 3 = (B,0,1)
======================
Matrix element storage
======================
Terms
-1*C^+(0)C(0) + -1*C^+(0)C(2) + -1*C^+(1)C(1) + -1*C^+(1)C(3) + -1*C^+(2)C(0) + -1*C^+(2)C(2) + -1*C^+(3)C(1) + -1*C^+(3)C(3) + -2*C^+(0)C^+(1)C(0)C(1) + -2*C^+(2)C^+(3)C(2)C(3)
N terms
1*C^+(0)C(0) + 1*C^+(1)C(1) + 1*C^+(2)C(2) + 1*C^+(3)C(3)
H commutes with N
[ H ,1*C^+(0)C(0) + 1*C^+(1)C(1) + 1*C^+(2)C(2) + 1*C^+(3)C(3) ]=0
[ H ,-0.5*C^+(0)C(0) + 0.5*C^+(1)C(1) + -0.5*C^+(2)C(2) + 0.5*C^+(3)C(3) ]=0
Preparing Hamiltonian parts...Calculating 9 jobs using 1 procs.
Calculating 9 jobs using 1 procs.
[4/9] P0 : part 3 [4] run;
[2/9] P0 : part 1 [2] run;
[3/9] P0 : part 2 [2] run;
[6/9] P0 : part 5 [2] run;
[8/9] P0 : part 7 [2] run;
[1/9] P0 : part 0 [1] run;
[5/9] P0 : part 4 [1] run;
[7/9] P0 : part 6 [1] run;
[9/9] P0 : part 8 [1] run;
done.
The value of ground energy is -3.23607
CreationOperator_1: 6 parts will be computed
Computing 1*C^+(1) in eigenbasis of the Hamiltonian: 0 16 33 50 66 83
AnnihilationOperator_1: 6 parts will be computed
Computing 1*C(1) in eigenbasis of the Hamiltonian: 0 16 33 50 66 83
0 | (-5.9535e-17,-0.184554)
1 | (-3.51059e-17,-0.373873)
2 | (-2.71198e-17,-0.37882)
3 | (-2.1774e-18,-0.3349)
4 | (-9.39264e-18,-0.289338)
5 | (-1.58814e-17,-0.251146)
6 | (-7.4351e-18,-0.220407)
7 | (-1.4935e-17,-0.195678)
8 | (-9.70438e-18,-0.17557)
9 | (-7.68787e-18,-0.158998)
TwoParticleGF(1111): 24 parts will be calculated
Calculating 24 jobs using 1 procs.
[1/24] P0 : part 0 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
[2/24] P0 : part 1 [1] run;
Total 8+8=16 terms -> 4+3=7, tols = 1.11111e-07 (coeff), 1e-08 (res)
[3/24] P0 : part 2 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
[4/24] P0 : part 3 [1] run;
Total 8+8=16 terms -> 4+3=7, tols = 1.11111e-07 (coeff), 1e-08 (res)
[5/24] P0 : part 4 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[6/24] P0 : part 5 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[7/24] P0 : part 6 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[8/24] P0 : part 7 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[9/24] P0 : part 8 [1] run;
Total 8+8=16 terms -> 8+7=15, tols = 1.11111e-07 (coeff), 1e-08 (res)
[10/24] P0 : part 9 [1] run;
Total 8+8=16 terms -> 8+7=15, tols = 1.11111e-07 (coeff), 1e-08 (res)
[11/24] P0 : part 10 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
[12/24] P0 : part 11 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
[13/24] P0 : part 12 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[14/24] P0 : part 13 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[15/24] P0 : part 14 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[16/24] P0 : part 15 [1] run;
Total 128+122=250 terms -> 94+96=190, tols = 8.13008e-09 (coeff), 1e-08 (res)
[17/24] P0 : part 16 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
[18/24] P0 : part 17 [1] run;
Total 8+8=16 terms -> 8+7=15, tols = 1.11111e-07 (coeff), 1e-08 (res)
[19/24] P0 : part 18 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
[20/24] P0 : part 19 [1] run;
Total 8+8=16 terms -> 8+7=15, tols = 1.11111e-07 (coeff), 1e-08 (res)
[21/24] P0 : part 20 [1] run;
Total 8+8=16 terms -> 4+3=7, tols = 1.11111e-07 (coeff), 1e-08 (res)
[22/24] P0 : part 21 [1] run;
Total 8+8=16 terms -> 4+3=7, tols = 1.11111e-07 (coeff), 1e-08 (res)
[23/24] P0 : part 22 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
[24/24] P0 : part 23 [1] run;
Total 8+8=16 terms -> 6+7=13, tols = 1.11111e-07 (coeff), 1e-08 (res)
done.
-2 -2 -2|(0,0)
-2 -2 -1|(0,0)
-2 -2 0|(0,0)
-2 -2 1|(0,0)
-2 -1 -2|(0,0)
-2 -1 -1|(0,0)
-2 -1 0|(0,0)
-2 -1 1|(0,0)
-2 0 -2|(0,0)
-2 0 -1|(0,0)
-2 0 0|(0,0)
-2 0 1|(0,0)
-2 1 -2|(0,0)
-2 1 -1|(0,0)
-2 1 0|(0,0)
-2 1 1|(0,0)
-1 -2 -2|(0,0)
-1 -2 -1|(0,0)
-1 -2 0|(0,0)
-1 -2 1|(0,0)
-1 -1 -2|(0,0)
-1 -1 -1|(0,0)
-1 -1 0|(0,0)
-1 -1 1|(0,0)
-1 0 -2|(0,0)
-1 0 -1|(0,0)
-1 0 0|(0,0)
-1 0 1|(0,0)
-1 1 -2|(0,0)
-1 1 -1|(0,0)
-1 1 0|(0,0)
-1 1 1|(0,0)
0 -2 -2|(0,0)
0 -2 -1|(0,0)
0 -2 0|(0,0)
0 -2 1|(0,0)
0 -1 -2|(0,0)
0 -1 -1|(0,0)
0 -1 0|(0,0)
0 -1 1|(0,0)
0 0 -2|(0,0)
0 0 -1|(0,0)
0 0 0|(0,0)
0 0 1|(0,0)
0 1 -2|(0,0)
0 1 -1|(0,0)
0 1 0|(0,0)
0 1 1|(0,0)
1 -2 -2|(0,0)
1 -2 -1|(0,0)
1 -2 0|(0,0)
1 -2 1|(0,0)
1 -1 -2|(0,0)
1 -1 -1|(0,0)
1 -1 0|(0,0)
1 -1 1|(0,0)
1 0 -2|(0,0)
1 0 -1|(0,0)
1 0 0|(0,0)
1 0 1|(0,0)
1 1 -2|(0,0)
1 1 -1|(0,0)
1 1 0|(0,0)
1 1 1|(0,0)
Hello,
i get an error while trying to compile the tutorial. The error massage is:
CMake Error: The following variables are used in this project, but they are set to NOTFOUND.
Please set them or make sure they are set and tested correctly in the CMake files:
pomerol_DEP_LIBRARIES
regards
Arthur
This freezes for 160 cores.
mpirun -machinefile $TMPDIR/machines -np $NSLOTS anderson_pp_shift.cxx11.pomerol --U 1.0 --ed -0.5 --beta 26 --levels 0.997606403047774 0.142386656471943 -0.997606403047774 -0.142386656471943 --hoppings 0.243593970410131 0.227845830863211 0.243593970410131 0.227845830863211 --calc_gf 1 --calc_2pgf 1 --2pgf.indices 0 1 0 1 --2pgf.coeff_tol 1e-12 --2pgf.reduce_tol 1e-5 --wf_min -50 --wf_max 50 --wb_min -75 --wb_max 75
for executable https://gist.github.com/aeantipov/86b9a77c81d10680677339799c178307
Seems to work for small number of bosonic freqs.
Copied from pomerol-ed/pomerol2triqs#3
Dear Igor,
At present, only Sz is used for state classification as in the default mode of pomerol. In the Slater Hamiltonian, for example, Lz (w/o SO) or Jz (w/ SO) could be additionally used to reduce the block size.
Is there any way to pass an Operator op to call symm.checkSymmetry(op)? Or, if not, which is the easiest way to extend the code?
It seems for me that one should extend the function pomerol_ed::diagonalize to be able to pass a list of operators that is used for additional symmetry check.
Best regards,
Junya
First of all, I would like to thank Junya @j-otsuki for his major contribution! The ability to compute susceptibilities has certainly been a much requested feature.
Today I discovered a compilation failure seen only in the POMEROL_COMPLEX_MATRIX_ELEMENT=ON
mode.
/home/igor/Physics/pomerol/pomerol.git/src/pomerol/SusceptibilityPart.cpp: In member function ‘void Pomerol::SusceptibilityPart::compute()’:
/home/igor/Physics/pomerol/pomerol.git/src/pomerol/SusceptibilityPart.cpp:68:36: error: no match for ‘operator+=’ (operand types are ‘Pomerol::RealType’ {aka ‘double’} and ‘std::complex<double>’)
ZeroPoleWeight += Ainner.value() * Binner.value() * DMpartOuter.getWeight(index1);
~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
I guess putting an std::real()
around the RHS would make the error go away, but the problem is actually deeper than that. ZeroPoleWeight
is declared to be real, but this property is guaranteed only when operator B
is the Hermitian conjugate of A
(if I am not mistaken).
Therefore, we should either declare ZeroPoleWeight
as MelemType
, or check that B = A^+
in the constructor of Susceptibility
.
Perhaps use a template parameter instead and compile both. Or just simply make it complex altogether (any spin-orbit interaction needs it anyway)
Dear Andrey,
I'm computing two-particle Green's functions for multi-orbital models. As you know, it is very costly. Since two-particle GF has a lot of components in multi-orbital models (N_orb^4 where N_orb is the number of orbitals), it would be efficient to use MPI for the loop of the components. I can do it outside of the pomerol library (actually in a python wrapper), but probably at the same time, I have to disable MPI in the TwoParticleGF class.
Is my understanding correct? And, could you tell me how to do it? If I understand correctly, I need to modify only TwoParticleGF::compute() and skip using pMPI::mpi_skel in some way.
Just for your information, a similar question was raised recently in pomerol-ed/pomerol2triqs#5.
Best regards,
Junya Otsuki
Boost::program_options is incompatible with old gcc, clang and builds fail
This issue was discovered by Sasha Lichtenstein while he was trying to build pomerol2triqs
on his MacBook Pro using Boost 1.72.
CMake was issuing the following error message,
CMake Error at c++/CMakeLists.txt:1 (add_library):
Target "pomerol2triqs_c" links to target "Boost::mpi" but the target was
not found. Perhaps a find_package() call is missing for an IMPORTED
target, or an ALIAS target is missing?
The problem roots in the way pomerol::pomerol
CMake target is exported. The installed share/pomerol/pomerol.cmake
contains the following lines:
set_target_properties(pomerol::pomerol PROPERTIES
INTERFACE_INCLUDE_DIRECTORIES "/usr/include/eigen3;/usr/include;/usr/include;${_IMPORT_PREFIX}/include"
INTERFACE_LINK_LIBRARIES "/usr/lib64/libmpi_cxx.so;/usr/lib64/libmpi.so;Boost::mpi;Boost::serialization"
)
On my own Linux laptop those lines are rather different and include explicit paths to the compiled Boost components.
set_target_properties(pomerol::pomerol PROPERTIES
INTERFACE_INCLUDE_DIRECTORIES "/usr/include/eigen3;/usr/include;/usr/include;${_IMPORT_PREFIX}/include"
INTERFACE_LINK_LIBRARIES "/usr/lib64/libmpi_cxx.so;/usr/lib64/libmpi.so;/usr/lib64/libboost_mpi-mt.so;/usr/lib64/libboost_serialization-mt.so"
)
I wonder if it's a duty of the consumer's CMake code to always import the Boost targets by calling find_package(Boost)
along with find_package(pomerol)
.
anderson.pomerol --U 1 --beta 26 --levels -0.677193904997332 -1.63229282488024 0.677193904997332 1.63229282488024 --hoppings 0.155286870457831 0.312708587859944 0.155286870457831 0.312708587859944 --calc_gf 1 --calc_2pgf 1 --2pgf.indices 0 1 0 1 --2pgf.coeff_tol 1e-12 --2pgf.reduce_tol 1e-5 --wf_min -20 --wf_max 20
in cxx11 mode produces non-zero imag part.
This is not related to tolerances - single site has the same problem.
Can be done using pre-commit
Dear Andrey,
Let me ask one question. Is there any way to compute the susceptibility defined by
chi(iw) = F < A(tau) B >
where iw is the bosonic Matsubara frequency, and F denotes the Fourier transform from tau to iw. More explicitly, what I want to compute is
chi_{ijkl}(iw) = F < c_i^+(tau) c_j(tau) c_k^+ c_l >
Best,
Junya
We're not using it much.
When I try to run anderson.pomerol
program as follows
mpirun -n 3 prog/bin/anderson.pomerol --calc_2pgf 1 --levels -1.0 0.0 1.0 --hoppings 1.0 1.0 1.0
it occasionally crashes with
/home/igor/Physics/pomerol/pomerol.git/src/pomerol/Hamiltonian.cpp:92: Worker3 didn't calculate part4
terminate called after throwing an instance of 'std::logic_error'
what(): Worker didn't calculate this part.
Evaluate if that's useful
Hey Andrey,
I am trying to build the current master branch on a CentOS 7.4 Machine with
gcc 7.3.0
eigen 3.3.4
boost 1.68
I am running into the following error during compilation.
It looks like at mpi_skel.hpp:97 you are trying to use boost::mpi::broadcast a std::vector<..> which requires vector to be serializeable.
[ 1%] Building CXX object CMakeFiles/pomerol.dir/src/pomerol/Hamiltonian.cpp.o
/cm/shared/sw/pkg/devel/gcc/7.3.0/bin/c++ -Dpomerol_EXPORTS -I/mnt/home/wentzell/Dropbox/Coding/pomerol/include -I/mnt/home/wentzell/Dropbox/Coding/pomerol/build/include -I/cm/shared/sw/pkg/devel/openmpi/1.10.6-hfi-slurm17/include -I/mnt/home/wentzell/opt/boost-1.68/include -I/mnt/home/wentzell/Dropbox/Coding/pomerol/build/gtest/include -Wno-register -march=broadwell -std=c++11 -Wno-unused-local-typedefs -fopenmp -O3 -DNDEBUG -fPIC -o CMakeFiles/pomerol.dir/src/pomerol/Hamiltonian.cpp.o -c /mnt/home/wentzell/Dropbox/Coding/pomerol/src/pomerol/Hamiltonian.cpp
In file included from /mnt/home/wentzell/opt/boost-1.68/include/boost/serialization/split_member.hpp:23:0,
from /mnt/home/wentzell/opt/boost-1.68/include/boost/serialization/nvp.hpp:26,
from /mnt/home/wentzell/opt/boost-1.68/include/boost/serialization/complex.hpp:23,
from /mnt/home/wentzell/Dropbox/Coding/pomerol/include/pomerol/Misc.h:28,
from /mnt/home/wentzell/Dropbox/Coding/pomerol/include/pomerol/Hamiltonian.h:10,
from /mnt/home/wentzell/Dropbox/Coding/pomerol/src/pomerol/Hamiltonian.cpp:1:
/mnt/home/wentzell/opt/boost-1.68/include/boost/serialization/access.hpp: In instantiation of 'static void boost::serialization::access::serialize(Archive&, T&, unsigned int) [with Archive = boost::mpi::packed_oarchive; T = std::vector<int>]':
/mnt/home/wentzell/opt/boost-1.68/include/boost/serialization/serialization.hpp:68:22: required from 'void boost::serialization::serialize(Archive&, T&, unsigned int) [with Archive = boost::mpi::packed_oarchive; T = std::vector<int>]'
/mnt/home/wentzell/opt/boost-1.68/include/boost/serialization/serialization.hpp:126:14: required from 'void boost::serialization::serialize_adl(Archive&, T&, unsigned int) [with Archive = boost::mpi::packed_oarchive; T = std::vector<int>]'
/mnt/home/wentzell/opt/boost-1.68/include/boost/archive/detail/oserializer.hpp:153:40: required from 'void boost::archive::detail::oserializer<Archive, T>::save_object_data(boost::archive::detail::basic_oarchive&, const void*) const [with Archive = boost::mpi::packed_oarchive; T = std::vector<int>]'
/mnt/home/wentzell/opt/boost-1.68/include/boost/archive/detail/oserializer.hpp:106:1: required from 'class boost::archive::detail::oserializer<boost::mpi::packed_oarchive, std::vector<int> >'
/mnt/home/wentzell/opt/boost-1.68/include/boost/archive/detail/oserializer.hpp:258:13: required from 'static void boost::archive::detail::save_non_pointer_type<Archive>::save_standard::invoke(Archive&, const T&) [with T = std::vector<int>; Archive = boost::mpi::packed_oarchive]'
/mnt/home/wentzell/opt/boost-1.68/include/boost/archive/detail/oserializer.hpp:315:22: [ skipping 4 instantiation contexts, use -ftemplate-backtrace-limit=0 to disable ]
/mnt/home/wentzell/opt/boost-1.68/include/boost/mpi/packed_oarchive.hpp:112:5: required from 'void boost::mpi::packed_oarchive::save_override(const T&) [with T = std::vector<int>]'
/mnt/home/wentzell/opt/boost-1.68/include/boost/archive/detail/interface_oarchive.hpp:70:9: required from 'Archive& boost::archive::detail::interface_oarchive<Archive>::operator<<(const T&) [with T = std::vector<int>; Archive = boost::mpi::packed_oarchive]'
/mnt/home/wentzell/opt/boost-1.68/include/boost/mpi/collectives/broadcast.hpp:113:12: required from 'void boost::mpi::detail::broadcast_impl(const boost::mpi::communicator&, T*, int, int, mpl_::false_) [with T = std::vector<int>; mpl_::false_ = mpl_::bool_<false>]'
/mnt/home/wentzell/opt/boost-1.68/include/boost/mpi/collectives/broadcast.hpp:141:25: required from 'void boost::mpi::broadcast(const boost::mpi::communicator&, T&, int) [with T = std::vector<int>]'
/mnt/home/wentzell/Dropbox/Coding/pomerol/include/mpi_dispatcher/mpi_skel.hpp:97:30: required from 'std::map<int, int> pMPI::mpi_skel<WrapType>::run(const boost::mpi::communicator&, bool) [with WrapType = pMPI::PrepareWrap<Pomerol::HamiltonianPart>]'
/mnt/home/wentzell/Dropbox/Coding/pomerol/src/pomerol/Hamiltonian.cpp:34:72: required from here
/mnt/home/wentzell/opt/boost-1.68/include/boost/serialization/access.hpp:116:11: error: 'class std::vector<int>' has no member named 'serialize'
t.serialize(ar, file_version);
I have configured cmake with
cmake ../ -DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=$HOME/opt/pomerol -DProgs=ON -DPOMEROL_COMPLEX_MATRIX_ELEMENTS=ON -DPOMEROL_USE_OPENMP=ON -DCXX11=ON -DTesting=ON
Hi,
I'm currently having trouble making pomerol. During make, I get the following errors:
[ 48%] Linking CXX executable FieldOperatorTest
../libpomerol.so: undefined reference to boost::mpi::detail::packed_archive_recv(int, int, int, boost::mpi::packed_iarchive&, MPI_Status&)' ../libpomerol.so: undefined reference to
boost::mpi::communicator::operator int() const'
../libpomerol.so: undefined reference to `boost::mpi::detail::packed_archive_send(int, int, int, boost::mpi::packed_oarchive const&)'
The most obvious source for errors would be the boost version ( 1.58.0 on this machine). I am trying to install a newer version of boost to see if that helps (but installing boost is slow...). Do you know what the minimal required version of boost is / which version are you usually using? Do you see other obvious things that could be going wrong?
Thanks in advance,
Erik
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