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- /**********************************************************
-
- This software is part of J.-S. Caux's ABACUS library.
-
- Copyright (c) J.-S. Caux.
-
- -----------------------------------------------------------
-
- File: LiebLin_Fourier_to_x_equal_t.cc
-
- Purpose: Fourier transform to static space correlator for LiebLin.
-
- ***********************************************************/
-
- #include "ABACUS.h"
-
- using namespace std;
- using namespace ABACUS;
-
-
- int main(int argc, char* argv[])
- {
- if (argc != 9) { // provide some info
-
- cout << endl << "Welcome to ABACUS\t(copyright J.-S. Caux)." << endl;
- cout << endl << "Usage of LiebLin_Fourier_to_x_equal_t executable: " << endl;
- cout << endl << "Provide the following arguments:" << endl << endl;
- cout << "char whichDSF \t\t Which structure factor ? Options are: d for rho rho, g for psi psi{dagger}, o for psi{dagger} psi" << endl;
- cout << "DP c_int \t\t Value of the interaction parameter" << endl;
- cout << "DP L \t\t\t Length of the system" << endl;
- cout << "int N \t\t\t Number of particles" << endl;
- cout << "int iKmin" << endl << "int iKmax \t\t Min and max momentum integers scanned over" << endl;
- cout << "DP kBT \t\t Temperature" << endl;
- cout << "int Npts_x Number of points in space for the Fourier transform" << endl;
- }
-
- else { // (argc == 9), correct nr of arguments
- char whichDSF = *argv[1];
- DP c_int = atof(argv[2]);
- DP L = atof(argv[3]);
- int N = atoi(argv[4]);
- int iKmin = atoi(argv[5]);
- int iKmax = atoi(argv[6]);
- DP kBT = atof(argv[7]);
- int Npts_x = atoi(argv[8]);
- // Force Npts_x
- //Npts_x = L;
-
- stringstream filenameprefix;
- Data_File_Name (filenameprefix, whichDSF, c_int, L, N, iKmin, iKmax, kBT, 0.0, "");
- string prefix = filenameprefix.str();
-
- stringstream RAW_stringstream; string RAW_string;
- RAW_stringstream << prefix << ".raw";
- RAW_string = RAW_stringstream.str(); const char* RAW_Cstr = RAW_string.c_str();
- ifstream RAW_infile;
- RAW_infile.open(RAW_Cstr);
- if (RAW_infile.fail()) {
- cout << RAW_Cstr << endl;
- ABACUSerror("Could not open RAW_infile... ");
- }
-
- // We also read the f-sumrule file, to correct for missing intensity.
- stringstream FSR_stringstream; string FSR_string;
- FSR_stringstream << prefix << ".fsr";
- FSR_string = FSR_stringstream.str(); const char* FSR_Cstr = FSR_string.c_str();
- ifstream FSR_infile;
- FSR_infile.open(FSR_Cstr);
- if (FSR_infile.fail()) {
- cout << FSR_Cstr << endl;
- ABACUSerror("Could not open FSR_infile... ");
- }
-
- stringstream SFT_stringstream; string SFT_string;
- SFT_stringstream << prefix << ".sft";
- SFT_string = SFT_stringstream.str(); const char* SFT_Cstr = SFT_string.c_str();
- ofstream SFT_outfile;
- SFT_outfile.open(SFT_Cstr);
- if (SFT_outfile.fail()) ABACUSerror("Could not open SFT_outfile... ");
-
- // First compute the static structure factor from the RAW data:
-
- Vect_DP SSF(0.0, iKmax - iKmin + 1);
-
- DP omega;
- int iK;
- DP FF;
- //int conv;
- DP dev;
- string label;
-
- while (RAW_infile.peek() != EOF) {
- RAW_infile >> omega >> iK >> FF >> dev >> label;
- if (iK >= iKmin && iK <= iKmax) {
- SSF[iK - iKmin] += FF * FF;
- }
- }
- RAW_infile.close();
-
- // Reset proper normalization:
- DP normalization = twoPI * L;
- for (int iK = 0; iK < iKmax - iKmin + 1; ++iK) SSF[iK] *= normalization/twoPI; // twoPI from integral over omega
-
- // We now refine the SSF in the following way.
- // First, we read off the f-sumrule saturation from the FSR file.
- // Then, we put back the missing weight, assuming that it lives
- // on the free k^2 dispersion relation (so the DSF is then simply 2\pi N/L \delta(\omega - k^2)).
-
- Vect_DP FSRsaturated(0.0, iKmax - iKmin + 1);
- int dummyint;
- DP dummy;
- for (int i = iKmin; i <= iKmax; ++i)
- FSR_infile >> dummyint >> FSRsaturated[i - iKmin] >> dummy;
-
- FSR_infile.close();
-
- // Now correct the SSF by the missing piece:
- //for (int iK = iKmin; iK <= iKmax; ++iK)
- //SSF[iK - iKmin] += (1.0 - FSRsaturated[iK - iKmin]) * N/L;
-
- //cout << FSRsaturated << endl;
-
- //cout << SSF << endl;
-
- // Now define real-space coordinates: between 0 and L
- Vect_DP xlattice(Npts_x);
- for (int i = 0; i < Npts_x; ++i) xlattice[i] = (i + 0.5) * L/Npts_x;
-
- // Now the correlation at x:
- Vect_DP FTre(0.0, Npts_x);
- Vect_DP FTim(0.0, Npts_x);
-
- DP twopioverL = twoPI/L;
-
- // Fourier transform:
- for (int ix = 0; ix < Npts_x; ++ix) {
- for (int iK = iKmin; iK <= iKmax; ++iK) {
- FTre[ix] += SSF[iK - iKmin] * cos(twopioverL * iK * xlattice[ix]);
- FTim[ix] += SSF[iK - iKmin] * sin(twopioverL * iK * xlattice[ix]);
- }
- // Reset proper normalization: 1/L from space FT,
- FTre[ix] /= L;
- FTim[ix] /= L;
-
- // Outside of window iKmin, iKmax, we take the DSF to be a constant with delta function
- // at free energy k^2, so DSF = 2\pi N/L \delta(\omega - k^2) (to fit f-sumrule)
- // so SSF becomes N/L.
- // We thus need to correct above by adding
- // \frac{1}{L} \sum_{-\infty}^{iKmin - 1} SSF e^{ikx} + \frac{1}{L} \sum_{iKmax + 1}^\infty SSF e^{ikx}
- // Resumming carefully:
- if (whichDSF == 'd') {
- FTre[ix] += (sin(twopioverL * (iKmin - 0.5) * xlattice[ix]) - sin(twopioverL * (iKmax + 0.5) * xlattice[ix]))
- * N/(2.0 * L*L * sin(PI * xlattice[ix]/L));
- FTim[ix] += (-cos(twopioverL * (iKmin - 0.5) * xlattice[ix]) + cos(twopioverL * (iKmax + 0.5) * xlattice[ix]))
- * N/(2.0 * L*L * sin(PI * xlattice[ix]/L));
- }
- }
-
- // Since iKmax and iKmin are finite, we need to average over an interval of
- // deltax such that (2\pi/L) iKmax deltax = 2\pi, with deltax == deltaix * L/Npts_x
- // so deltaix = (Npts_x/L) * (L/iKmax)
- /*
- int deltaix = 0*int(Npts_x/(2.0*iKmax));
- cout << "deltaix = " << deltaix << endl;
-
- Vect_DP FTreavg(0.0, Npts_x);
- Vect_DP FTimavg(0.0, Npts_x);
- for (int ix = 0; ix < Npts_x; ++ix) {
- for (int ix2 = -deltaix; ix2 < deltaix; ++ix2) {
- FTreavg[ix] += FTre[ABACUS::min(ABACUS::max(0, ix + ix2), Npts_x - 1)];
- FTimavg[ix] += FTim[ABACUS::min(ABACUS::max(0, ix + ix2), Npts_x - 1)];
- }
- FTreavg[ix] /= (2*deltaix + 1);
- FTimavg[ix] /= (2*deltaix + 1);
- }
- */
- if (whichDSF == 'd') cout << "g2(0) = dE0_dc/L = " << LiebLin_dE0_dc (c_int, L, N)/L << "\t" << LiebLin_dE0_dc (c_int, 2.0*L, 2*N)/(2.0*L) << endl;
-
- // Output to file:
- for (int ix = 0; ix < Npts_x; ++ix) {
- if (ix > 0) SFT_outfile << endl;
- //SFT_outfile << xlattice[ix] << "\t" << FTre[ix] << "\t" << FTim[ix] << "\t" << FTreavg[ix] << "\t" << FTimavg[ix];
- SFT_outfile << xlattice[ix] << "\t" << FTre[ix] << "\t" << FTim[ix];
- }
-
- SFT_outfile.close();
- }
-
- return(0);
-
- }
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