Include first version of test Rho = Psidag Psi for LiebLin
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J.-S. Caux
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@ -34,11 +34,11 @@ namespace ABACUS {
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// Types of descendents:
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// 14 == iK stepped up, leading exc one step further (can lead to ph recombination)
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// 13 == iK stepped up, next exc (nr of ph preserved, not taking possible ph recombination into account)
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// 12 == iK stepped up, next ext (nr ph increased, not taking possible ph recombination into account)
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// 11 == iK stepped down, leading exc one step further (can lead to ph recombination)
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// 10 == iK stepped down, next exc (nr of ph preserved, not taking possible ph recombination into account)
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// 9 == iK stepped down, next exc (nr ph increased, not taking possible ph recombination into account)
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// 13 == iK up, next exc (nr of ph preserved, not taking possible ph recombination into account)
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// 12 == iK up, next ext (nr ph increased, not taking possible ph recombination into account)
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// 11 == iK down, leading exc one step further (can lead to ph recombination)
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// 10 == iK down, next exc (nr of ph preserved, not taking possible ph recombination into account)
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// 9 == iK down, next exc (nr ph increased, not taking possible ph recombination into account)
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// 8 == iK preserved, 14 and 11 (up to 2 ph recombinations)
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// 7 == iK preserved, 14 and 10
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// 6 == iK preserved, 14 and 9
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@ -50,8 +50,10 @@ namespace ABACUS {
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// 0 == iK preserved, 12 and 9
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// For scanning over symmetric states, the interpretation is slightly different.
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// Types 14, 13 and 12 step iK up using the Ix2 on the right only, and mirrors the change on the left Ix2.
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// Types 11, 10 and 9 step iK down using the Ix2 on the right only, and mirrors the change on the left Ix2.
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// Types 14, 13 and 12 step iK up using the Ix2 on the right only,
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// and mirrors the change on the left Ix2.
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// Types 11, 10 and 9 step iK down using the Ix2 on the right only,
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// and mirrors the change on the left Ix2.
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// There is then no need of scanning over types 0 - 8.
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// By convention, types 9, 10 and 11 can call types 9 - 14; types 12-14 can only call types 12-14.
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@ -61,7 +63,8 @@ namespace ABACUS {
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// This function returns true if descending further can lead to a particle-hole recombination.
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// The criteria which are used are:
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// - the active excitation has moved at least one step (so it has already created its p-h pair)
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// - there exists an OriginIx2 between the active Ix2 and the next Ix2 (to right or left depending on type of descendent)
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// - there exists an OriginIx2 between the active Ix2 and the next Ix2
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// (to right or left depending on type of descendent)
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Vect<Vect<int> > ScanIx2 = Return_Ix2_from_Label (ScanIx2_label, OriginIx2);
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@ -71,7 +74,7 @@ namespace ABACUS {
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bool excfound = false;
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do {
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exclevel++;
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if (exclevel == ScanIx2.size()) { // there isn't a single right-moving quantum number in ScanIx2
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if (exclevel == ScanIx2.size()) { // there is no right-moving quantum number in ScanIx2
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break;
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}
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for (int alpha = 0; alpha < ScanIx2[exclevel].size(); ++alpha)
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@ -125,7 +128,8 @@ namespace ABACUS {
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// This function returns true if descending further can lead to a particle-hole recombination.
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// The criteria which are used are:
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// - the active excitation has moved at least one step (so it has already created its p-h pair)
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// - there exists an OriginIx2 between the active Ix2 and the next Ix2 (to right or left depending on type of descendent)
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// - there exists an OriginIx2 between the active Ix2 and the next Ix2
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// (to right or left depending on type of descendent)
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Vect<Vect<int> > ScanIx2 = Return_Ix2_from_Label (ScanIx2_label, OriginIx2);
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@ -153,7 +157,8 @@ namespace ABACUS {
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if (excfound && !BaseScanIx2[exclevel].includes(ScanIx2[exclevel][excindex])) {
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// there exists an already dispersing excitation which isn't in Origin
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// Is there a possible recombination?
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if (excindex > 0) { // a particle to the left of excitation has already moved left, so there is a hole
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if (excindex > 0) {
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// a particle to the left of excitation has already moved left, so there is a hole
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// check that there exists an occupied Ix2 in Origin sitting between the excitation
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// and the next Ix2 to its left in ScanIx2
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for (int alpha = 0; alpha < BaseScanIx2[exclevel].size(); ++alpha)
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@ -227,13 +232,18 @@ namespace ABACUS {
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int Max_Secs_alert = int(0.95 * Max_Secs); // we break any ongoing ithread loop beyond this point
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stringstream filenameprefix;
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Data_File_Name (filenameprefix, whichDSF, iKmin, iKmax, kBT, AveragingState, SeedScanState, defaultScanStatename);
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Data_File_Name (filenameprefix, whichDSF, iKmin, iKmax, kBT,
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AveragingState, SeedScanState, defaultScanStatename);
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if (in_parallel) for (int r = 0; r < paralevel; ++r) filenameprefix << "_" << rank[r] << "_" << nr_processors[r];
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if (in_parallel)
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for (int r = 0; r < paralevel; ++r)
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filenameprefix << "_" << rank[r] << "_" << nr_processors[r];
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string prefix = filenameprefix.str();
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stringstream filenameprefix_prevparalevel; // without the rank and nr_processors of the highest paralevel
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stringstream filenameprefix_prevparalevel;
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// without the rank and nr_processors of the highest paralevel
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Data_File_Name (filenameprefix_prevparalevel, whichDSF, iKmin, iKmax, kBT,
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AveragingState, SeedScanState, defaultScanStatename);
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if (in_parallel) for (int r = 0; r < paralevel - 1; ++r)
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@ -330,7 +340,7 @@ namespace ABACUS {
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ScanStateList.Populate_List(whichDSF, SeedScanState);
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if (refine && !in_parallel) ScanStateList.Load_Info (SUM_Cstr);
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else if (in_parallel && rank.sum() == 0) {}; // do nothing, keep the info in the higher .sum file!
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else if (in_parallel && rank.sum() == 0) {}; // do nothing, keep info in the higher .sum file!
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DP Chem_Pot = Chemical_Potential (AveragingState);
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DP sumrule_factor = Sumrule_Factor (whichDSF, AveragingState, Chem_Pot, iKmin, iKmax);
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@ -342,8 +352,8 @@ namespace ABACUS {
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int Ndata_previous_cycle = 0;
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int ninadm = 0; // number of inadmissible states for which we save some info in .inadm file. Save first 1000.
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int nconv0 = 0; // number of unconverged states for which we save some info in .conv0 file. Save first 1000.
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int ninadm = 0; // nr of inadm states for which we save info in .inadm file. Save first 1000.
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int nconv0 = 0; // nr of unconv states for which we save info in .conv0 file. Save first 1000.
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double start_time_omp = omp_get_wtime();
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double current_time_omp = omp_get_wtime();
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@ -373,12 +383,14 @@ namespace ABACUS {
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double start_time_flags = omp_get_wtime();
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// First flag the new base/type 's that we need to include:
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ScanStateList.Raise_Scanning_Flags (exp(-paused_thread_data.logscale * paused_thread_data.lowest_il_with_nthreads_neq_0));
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ScanStateList.Raise_Scanning_Flags
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(exp(-paused_thread_data.logscale * paused_thread_data.lowest_il_with_nthreads_neq_0));
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// Get these base/type started:
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for (int i = 0; i < ScanStateList.ndef; ++i) {
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if (ScanStateList.flag_for_scan[i] && ScanStateList.info[i].Ndata == 0 && !ScanStateList.scan_attempted[i]) {
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if (ScanStateList.flag_for_scan[i] && ScanStateList.info[i].Ndata == 0
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&& !ScanStateList.scan_attempted[i]) {
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Scan_Info scan_info_flags;
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@ -0,0 +1,186 @@
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/**********************************************************
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This software is part of J.-S. Caux's ABACUS library.
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Copyright (c) J.-S. Caux.
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-----------------------------------------------------------
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File: ln_Density_ME.cc
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Purpose: Computes the density operator \rho(x = 0) matrix element
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***********************************************************/
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#include "ABACUS.h"
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using namespace std;
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using namespace ABACUS;
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/**
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The matrix elements of \f$\hat{\rho}(x=0)\f$ and \f$\Psi^\dagger (x=0) \Psi(x=0)\f$
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are compared between two random bra and ket states. The density matrix element is
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directly computed from the determinant representation. The field operator product is
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computed by introducing a resolution of the identity. The function outputs the degree
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of accuracy achieved.
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*/
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int main()
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{
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DP c_int = 4.344;
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DP L = 8.0;
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int N = 8;
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DP kBT = 8.0;
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int DiKmax = 10*N;
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// Use a thermal state to get some nontrivial distribution
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//LiebLin_Bethe_State spstate = Canonical_Saddle_Point_State (c_int, L, N, kBT);
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LiebLin_Bethe_State spstate (c_int, L, N);
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// spstate.Ix2[0] -= 8;
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// spstate.Ix2[1] -= 4;
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// spstate.Ix2[2] -= 2;
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// spstate.Ix2[N-3] += 2;
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// spstate.Ix2[N-2] += 4;
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// spstate.Ix2[N-1] += 6; // keep asymmetry
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spstate.Compute_All(true);
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//cout << setprecision(16) << spstate << endl;
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// Now define the anchor for scanning
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LiebLin_Bethe_State SeedScanState = Remove_Particle_at_Center (spstate);
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SeedScanState.Compute_All(true);
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//cout << setprecision(16) << SeedScanState << endl;
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// Map out the available unoccupied quantum nrs
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// We scan from Ix2min - DiKmax to Ix2max + DiKmax, and there are N-1 occupied, so there are
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int nr_par_positions = DiKmax + (SeedScanState.Ix2[N-2] - SeedScanState.Ix2[0])/2 + 1 - N + 1;
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Vect<int> Ix2_available (nr_par_positions);
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int nfound = 0;
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for (int i = SeedScanState.Ix2[0] - DiKmax; i <= SeedScanState.Ix2[N-2] + DiKmax; i += 2) {
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bool available = true;
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for (int j = 0; j < N-1; ++j)
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if (i == SeedScanState.Ix2[j]) {
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available = false;
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break;
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}
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if (available)
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Ix2_available[nfound++] = i;
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}
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if (nfound != nr_par_positions) {
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cout << "nround = " << nfound << "\tnr_par_positions = " << nr_par_positions << endl;
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ABACUSerror("Wrong number of particle positions found.");
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}
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// Define bra and ket states
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LiebLin_Bethe_State lstate = spstate;
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lstate.Ix2[0] -= 4;
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lstate.Ix2[1] -= 2;
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lstate.Compute_All(false);
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cout << setprecision(16) << lstate << endl;
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LiebLin_Bethe_State rstate = spstate;
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rstate.Ix2[N-1] += 8;
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rstate.Ix2[N-2] += 2;
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rstate.Compute_All(false);
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cout << setprecision(16) << rstate << endl;
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//lstate = rstate;
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// Matrix element to reproduce
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complex<DP> ln_rho_ME = ln_Density_ME(lstate, rstate);
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cout << "ln_Density_ME = " << ln_rho_ME << endl;
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// We now do hard-coded scanning of up to fixed nr of particle-hole pairs
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complex<DP> Psidag_Psi = 0.0;
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LiebLin_Bethe_State scanstate = SeedScanState;
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// Zero particle-hole:
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scanstate = SeedScanState;
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Psidag_Psi += exp(conj(ln_Psi_ME(scanstate, lstate)) + ln_Psi_ME(scanstate, rstate));
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cout << "Ratio Rho/PsidagPsi After scanning 0 p-h: "
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<< setprecision(16) << real(Psidag_Psi/exp(ln_rho_ME))
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<< "\t" << imag(Psidag_Psi/exp(ln_rho_ME)) << endl;
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// One particle-hole:
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char a;
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for (int ih1 = 0; ih1 < N-1; ++ih1)
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for (int ipar1 = 0; ipar1 < nr_par_positions - 1; ++ipar1) {
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scanstate = SeedScanState;
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scanstate.Ix2[ih1] = Ix2_available[ipar1];
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scanstate.Ix2.QuickSort();
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scanstate.Compute_All(true);
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Psidag_Psi += exp(conj(ln_Psi_ME(scanstate, lstate)) + ln_Psi_ME(scanstate, rstate));
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// cout << "ih1 = " << ih1 << "\tipar1 = " << ipar1
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// << "\tPsidag_Psi = " << setprecision(16) << Psidag_Psi << endl;
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//cout << scanstate << endl;
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//cin >> a;
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}
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cout << "Ratio Rho/PsidagPsi After scanning 1 p-h: "
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<< setprecision(16) << real(Psidag_Psi/exp(ln_rho_ME))
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<< "\t" << imag(Psidag_Psi/exp(ln_rho_ME)) << endl;
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// Two particle-hole:
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for (int ih1 = 0; ih1 < N-2; ++ih1)
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for (int ih2 = ih1+1; ih2 < N-1; ++ih2)
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for (int ipar1 = 0; ipar1 < nr_par_positions - 2; ++ipar1) {
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for (int ipar2 = ipar1+1; ipar2 < nr_par_positions - 1; ++ipar2) {
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scanstate = SeedScanState;
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scanstate.Ix2[ih1] = Ix2_available[ipar1];
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scanstate.Ix2[ih2] = Ix2_available[ipar2];
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scanstate.Ix2.QuickSort();
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scanstate.Compute_All(true);
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Psidag_Psi += exp(conj(ln_Psi_ME(scanstate, lstate)) + ln_Psi_ME(scanstate, rstate));
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}
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}
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cout << "Ratio Rho/PsidagPsi After scanning 2 p-h: "
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<< setprecision(16) << real(Psidag_Psi/exp(ln_rho_ME))
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<< "\t" << imag(Psidag_Psi/exp(ln_rho_ME)) << endl;
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// Three particle-hole:
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for (int ih1 = 0; ih1 < N-3; ++ih1)
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for (int ih2 = ih1+1; ih2 < N-2; ++ih2)
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for (int ih3 = ih2+1; ih3 < N-1; ++ih3)
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for (int ipar1 = 0; ipar1 < nr_par_positions - 3; ++ipar1) {
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for (int ipar2 = ipar1+1; ipar2 < nr_par_positions - 2; ++ipar2) {
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for (int ipar3 = ipar2+1; ipar3 < nr_par_positions - 1; ++ipar3) {
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scanstate = SeedScanState;
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scanstate.Ix2[ih1] = Ix2_available[ipar1];
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scanstate.Ix2[ih2] = Ix2_available[ipar2];
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scanstate.Ix2[ih3] = Ix2_available[ipar3];
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scanstate.Ix2.QuickSort();
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scanstate.Compute_All(true);
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Psidag_Psi += exp(conj(ln_Psi_ME(scanstate, lstate)) + ln_Psi_ME(scanstate, rstate));
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}
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}
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// cout << "Ratio Rho/PsidagPsi while scanning 3 p-h: "
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// << setprecision(16) << real(Psidag_Psi/exp(ln_rho_ME))
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// << "\t" << imag(Psidag_Psi/exp(ln_rho_ME)) << endl;
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}
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cout << "Ratio Rho/PsidagPsi After scanning 3 p-h: "
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<< setprecision(16) << real(Psidag_Psi/exp(ln_rho_ME))
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<< "\t" << imag(Psidag_Psi/exp(ln_rho_ME)) << endl;
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return(0);
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}
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