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ABACUS/src/NRG/NRG_State_Selector.cc

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/**********************************************************
This software is part of J.-S. Caux's ABACUS library.
Copyright (c) J.-S. Caux.
-----------------------------------------------------------
File: NRG_State_Selector.cc
Purpose: select states for numerical RG method,
collaboration with Robert Konik.
***********************************************************/
#include "ABACUS.h"
using namespace std;
using namespace ABACUS;
namespace ABACUS {
DP Estimate_Contribution_of_Single_ph_Annihilation_Path_to_2nd_Order_PT (LiebLin_Bethe_State& TopState,
LiebLin_Bethe_State& GroundState,
Vect<complex <DP> >& FT_of_potential)
{
DP contrib_estimate = 0.0;
// Define OriginIx2 for labelling:
Vect<int> OriginIx2 = GroundState.Ix2;
// Calculate the number of particles in this state:
State_Label_Data topdata = Read_State_Label (TopState.label, OriginIx2);
int nphpairs = topdata.nexc[0];
if (nphpairs == 0) ABACUSerror("Trying to annihilate ground state in Estimate_Contribution...");
DP densityME = real(exp(ln_Density_ME (GroundState, TopState)));
if (is_nan(densityME)) {
cout << "ME is nan: label = " << TopState.label << endl;
ABACUSerror("ME didn't return value.");
}
int nr_cont = 0;
// Add first-order PT contribution, and 2nd order from ground state (V_{00} == 1)
contrib_estimate += abs(FT_of_potential[FT_of_potential.size()/2 + (TopState.iK - GroundState.iK)]
* (densityME/(GroundState.E - TopState.E))
* (1.0 - (GroundState.N/GroundState.L)/(GroundState.E - TopState.E)));
nr_cont++;
// Add second order PT contribution coming from TopState:
contrib_estimate += abs(FT_of_potential[FT_of_potential.size()/2 + 0]
* FT_of_potential[FT_of_potential.size()/2 + (TopState.iK - GroundState.iK)]
* 1.0 * densityME * (GroundState.N/GroundState.L) // 1.0 is V_{TopState, TopState}
/((GroundState.E - TopState.E) * (GroundState.E - TopState.E)));
nr_cont++;
// Now add 2nd order terms coming from single particle-hole annihilation paths:
// this is only to be included for states with at least 4 excitations (2 ph pairs)
if (nphpairs >= 2) {
for (int ipart = 0; ipart < nphpairs; ++ipart) {
for (int ihole = 0; ihole < nphpairs; ++ihole) {
LiebLin_Bethe_State DescendedState = TopState;
DescendedState.Annihilate_ph_pair(ipart, ihole, OriginIx2);
DescendedState.Compute_All(true);
DP densityME_top_desc = real(exp(ln_Density_ME (TopState, DescendedState)));
DP densityME_desc_ground = real(exp(ln_Density_ME (DescendedState, GroundState)));
// if intermediate state has momentum within allowable window, OK, otherwise discard contribution:
if (abs(TopState.iK - DescendedState.iK) < FT_of_potential.size()/2 &&
abs(DescendedState.iK - GroundState.iK) < FT_of_potential.size()/2) {
contrib_estimate += abs(FT_of_potential[FT_of_potential.size()/2 + (TopState.iK - DescendedState.iK)]
* FT_of_potential[FT_of_potential.size()/2 + (DescendedState.iK - GroundState.iK)]
* densityME_top_desc * densityME_desc_ground
/((GroundState.E - TopState.E) * (GroundState.E - DescendedState.E)));
nr_cont++;
}
if (nphpairs >= 3) { // go one step further
for (int ipart2 = ipart; ipart2 < nphpairs - 1; ++ipart2) {
for (int ihole2 = ihole; ihole2 < nphpairs - 1; ++ihole2) {
LiebLin_Bethe_State DescendedState2 = DescendedState;
DescendedState2.Annihilate_ph_pair(ipart2, ihole2, OriginIx2);
DescendedState2.Compute_All(true);
DP densityME_top_desc2 = real(exp(ln_Density_ME (TopState, DescendedState2)));
DP densityME_desc2_ground = real(exp(ln_Density_ME (DescendedState2, GroundState)));
// if intermediate state has momentum within allowable window, OK, otherwise discard contribution:
if (abs(TopState.iK - DescendedState2.iK) < FT_of_potential.size()/2 &&
abs(DescendedState2.iK - GroundState.iK) < FT_of_potential.size()/2) {
contrib_estimate += abs(FT_of_potential[FT_of_potential.size()/2 + (TopState.iK - DescendedState2.iK)]
* FT_of_potential[FT_of_potential.size()/2 + (DescendedState2.iK - GroundState.iK)]
* densityME_top_desc2 * densityME_desc2_ground
/((GroundState.E - TopState.E) * (GroundState.E - DescendedState2.E)));
nr_cont++;
}
if (nphpairs >= 4) { // go one step further
for (int ipart3 = ipart2; ipart3 < nphpairs - 2; ++ipart3) {
for (int ihole3 = ihole2; ihole3 < nphpairs - 2; ++ihole3) {
LiebLin_Bethe_State DescendedState3 = DescendedState2;
DescendedState3.Annihilate_ph_pair(ipart3, ihole3, OriginIx2);
DescendedState3.Compute_All(true);
DP densityME_top_desc3 = real(exp(ln_Density_ME (TopState, DescendedState3)));
DP densityME_desc3_ground = real(exp(ln_Density_ME (DescendedState3, GroundState)));
// if intermediate state has momentum within allowable window, OK, otherwise discard contribution:
if (abs(TopState.iK - DescendedState3.iK) < FT_of_potential.size()/2 &&
abs(DescendedState3.iK - GroundState.iK) < FT_of_potential.size()/2) {
contrib_estimate += abs(FT_of_potential[FT_of_potential.size()/2 + (TopState.iK - DescendedState3.iK)]
* FT_of_potential[FT_of_potential.size()/2
+ (DescendedState3.iK - GroundState.iK)]
* densityME_top_desc3 * densityME_desc3_ground
/((GroundState.E - TopState.E) * (GroundState.E - DescendedState3.E)));
nr_cont++;
}
} // for ihole3
} // for ipart3
} // if (nphpairs >= 4)
} // for ihole2
} // for ipart2
} // if (nphpairs >= 3)
} // for ihole
} // for ipart
} // if nphpairs >= 2
return(contrib_estimate);
}
void Select_States_for_NRG (DP c_int, DP L, int N, int iKmin, int iKmax, int Nstates_required,
bool symmetric_states, int iKmod, int weighing_option, Vect<complex <DP> >& FT_of_potential)
{
// This function reads an existing partition function file and determines whether
// each state is to be included in NRG by applying an energy, momentum and form factor criterion.
// The weighing function flag determines what kind of ordering is required:
// weighing_option == 0: ordering in energy
// weighing_option == 1: ordering according to perturbation theory in single p-h annihilation path
// weighing_option == 2: same as 1, but output of list is ordered in weight
stringstream filenameprefix;
Data_File_Name (filenameprefix, 'Z', c_int, L, N, iKmin, iKmax, 0.0, 0.0, "");
string prefix = filenameprefix.str();
stringstream RAW_stringstream; string RAW_string;
RAW_stringstream << prefix << ".raw";
stringstream NRG_stringstream; string NRG_string;
NRG_stringstream << "States_c_" << c_int << "_L_" << L << "_N_" << N
<< "_iKmin_" << iKmin << "_iKmax_" << iKmax << "_Nstates_" << Nstates_required
<< "_Sym_" << symmetric_states << "_iKmod_" << iKmod << "_wopt_" << weighing_option << ".nrg";
RAW_string = RAW_stringstream.str();
const char* RAW_Cstr = RAW_string.c_str();
NRG_string = NRG_stringstream.str();
const char* NRG_Cstr = NRG_string.c_str();
ifstream infile;
infile.open(RAW_Cstr);
if (infile.fail()) {
cout << RAW_Cstr << endl;
ABACUSerror("The input file was not opened successfully in Select_States_for_NRG. ");
}
ofstream NRG_outfile;
NRG_outfile.open(NRG_Cstr);
if (NRG_outfile.fail()) ABACUSerror("Could not open NRG_outfile... ");
NRG_outfile.precision(16);
// Read the whole data file:
// Count the number of entries in raw file:
int estimate_nr_entries = 0;
string line;
while (!infile.eof()) {
getline(infile, line);
estimate_nr_entries++;
}
const int MAXDATA = estimate_nr_entries;
DP* E = new DP[MAXDATA];
int* iK = new int[MAXDATA];
string* label = new string[MAXDATA];
bool* sym = new bool[MAXDATA];
int Ndata = 0;
infile.close();
infile.open(RAW_Cstr);
while (((infile.peek()) != EOF) && (Ndata < MAXDATA)) {
infile >> E[Ndata];
infile >> iK[Ndata];
infile >> label[Ndata];
Ndata++;
}
infile.close();
// Define the ground state:
LiebLin_Bethe_State GroundState (c_int, L, N);
GroundState.Compute_All(true);
// Define OriginIx2 for labelling:
Vect<int> OriginIx2 = GroundState.Ix2;
Scan_State_List<LiebLin_Bethe_State> ScanStateList ('d', GroundState);
// Build the momentum-dependent weight integral matrix:
// To cover negative and positive momenta (in case potential is not symmetric),
// we define the Weight_integral vector entry with index size/2 as corresponding to iK == 0.
// Calculate weight of states using selection criterion function
DP* weight = new DP[Ndata];
// For weighing using 2nd order PT, we only trace over 2 excitation states (1 p-h pair)
// Start by constructing these four classes once and for all:
for (int i = 0; i < Ndata; ++i) {
if (abs(iK[i]) % iKmod != 0) { // if iK not a multiple of iKmod: give stupidly high weight.
weight[i] = 1.0e+100;
sym[i] = false; // doesn't matter
}
else {
// Construct the state again, so that the density ME can be calculated
LiebLin_Bethe_State ScanState = ScanStateList.Return_State(Extract_Base_Label(label[i]));
ScanState.Set_to_Label (label[i]);
if (weighing_option == 1 || weighing_option == 2) ScanState.Compute_All(true);
sym[i] = ScanState.Check_Symmetry();
State_Label_Data currentdata = Read_State_Label (label[i], OriginIx2);
if (currentdata.nexc[0] == 0) weight[i] = 0.0;
else if (symmetric_states && iK[i] < 0 || iK[i] < iKmin || iK[i] > iKmax) weight[i] = 1.0e+100;
else if (symmetric_states && iK[i] == 0 && !sym[i]) {
// This state is at zero momentum but not symmetric. we keep it only if
// the first non-symmetric pair of quantum numbers is right-weighted:
int icheck = 0;
while (ScanState.Ix2[N-1-icheck] == -ScanState.Ix2[icheck]) icheck++;
if (ScanState.Ix2[N-1-icheck] > -ScanState.Ix2[icheck]) {
if (weighing_option == 0) weight[i] = E[i];
else if (weighing_option == 1 || weighing_option == 2)
weight[i] = 1.0/(1.0e-100 + fabs(Estimate_Contribution_of_Single_ph_Annihilation_Path_to_2nd_Order_PT
(ScanState, GroundState, FT_of_potential)));
}
else weight[i] = 1.0e+100;
}
else {
if (weighing_option == 0) weight[i] = E[i];
else if (weighing_option == 1 || weighing_option == 2)
weight[i] = 1.0/(1.0e-100 + fabs(Estimate_Contribution_of_Single_ph_Annihilation_Path_to_2nd_Order_PT
(ScanState, GroundState, FT_of_potential)));
}
}
} // for i
// Now order the states in increasing weight
int* index = new int[Ndata];
for (int i = 0; i < Ndata; ++i) index[i] = i;
QuickSort(weight, index, 0, Ndata - 1);
// Select states by increasing weight, with a max of Nstates_required entries
DP* E_kept = new DP[Nstates_required];
int* iK_kept = new int[Nstates_required];
string* label_kept = new string[Nstates_required];
bool* sym_kept = new bool[Nstates_required];
DP* weight_kept = new DP[Nstates_required];
// Copy selected states into new vectors:
for (int i = 0; i < ABACUS::min(Ndata, Nstates_required); ++i) {
E_kept[i] = E[index[i] ];
iK_kept[i] = iK[index[i] ];
//conv_kept[i] = conv[index[i] ];
label_kept[i] = label[index[i] ];
sym_kept[i] = sym[index[i] ];
weight_kept[i] = weight[i];
}
// If needed, order selected states by increasing energy:
int* index_kept = new int[Nstates_required];
for (int i = 0; i < Nstates_required; ++i) index_kept[i] = i;
if (weighing_option == 1) // only need to do this if energy ordering is chosen
QuickSort (E_kept, index_kept, 0, Nstates_required - 1);
// Output selected states:
for (int i = 0; i < Nstates_required; ++i) {
if (i > 0) NRG_outfile << endl;
NRG_outfile << i << "\t" << E_kept[i] << "\t" << iK_kept[index_kept[i] ]
<< "\t" << label_kept[index_kept[i] ]
<< "\t" << sym_kept[index_kept[i] ] << "\t" << weight_kept[index_kept[i] ];
}
delete[] E;
delete[] iK;
delete[] label;
delete[] sym;
delete[] E_kept;
delete[] iK_kept;
delete[] label_kept;
delete[] sym_kept;
delete[] weight;
NRG_outfile.close();
return;
}
} // namespace ABACUS
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