ABACUS/src/LIEBLIN/LiebLin_Sumrules.cc

/**********************************************************

This software is part of J.-S. Caux's ABACUS library.

Copyright (c) J.-S. Caux.

-----------------------------------------------------------

File:  src/LIEBLIN/LiebLin_Sumrules.cc

Purpose:  provides functions evaluating various sumrule factors
           for Lieb-Liniger.

***********************************************************/

#include "ABACUS.h"

using namespace std;
using namespace ABACUS;

namespace ABACUS {

  DP Sumrule_Factor (char whichDSF, LiebLin_Bethe_State& RefState, DP Chem_Pot, int iKmin, int iKmax)
  {
    DP sumrule_factor = 1.0;

    if (iKmin != iKmax) {
      if (whichDSF == 'Z') sumrule_factor = 1.0;
      else if (whichDSF == 'd' || whichDSF == '1') {

	// Here, we use a measure decreasing in K with K^2.
	// We sum up omega * MEsq/(iK^2) for all values of iKmin <= iK <= iKmax, discounting iK == 0 (where DSF vanishes)
	// We therefore have (N/L) x L^{-1} x (2\pi/L)^2 x (iKmax - iKmin + 1) = 4 \pi^2 x N x (iKmax - iKmin + 1)/L^4
	// Discounting iK == 0 (where DSF vanishes),
	// if iKmin <= 0 && iKmax >= 0 (in which case 0 is containted in [iKmin, iKmax])
	sumrule_factor = (iKmin <= 0 && iKmax >= 0) ?
	  (RefState.L * RefState.L * RefState.L * RefState.L)/(4.0 * PI * PI * RefState.N * (iKmax - iKmin))
	  : (RefState.L * RefState.L * RefState.L * RefState.L)/(4.0 * PI * PI * RefState.N * (iKmax - iKmin + 1));
      }
      // For the Green's function, it's the delta function \delta(x = 0) plus the density:
      else if (whichDSF == 'g')
	sumrule_factor = 1.0/((abs(iKmax - iKmin) + 1.0)/RefState.L + RefState.N/RefState.L);
      // For the one-body function, it's just the density:
      else if (whichDSF == 'o') sumrule_factor = RefState.L/RefState.N;
      else if (whichDSF == 'q') sumrule_factor = 1.0;
      else if (whichDSF == 'B') sumrule_factor = 1.0;
      else if (whichDSF == 'C') sumrule_factor = 1.0;
      else ABACUSerror("whichDSF option not consistent in Sumrule_Factor");
    }

    else if (iKmin == iKmax) {
      if (whichDSF == 'Z') sumrule_factor = 1.0;
      else if (whichDSF == 'd' || whichDSF == '1')
	// We sum up omega * MEsq
	sumrule_factor = pow(RefState.L, 4.0)/(4.0 * PI * PI * iKmax * iKmax * RefState.N);
      else if (whichDSF == 'g' || whichDSF == 'o') {
	// We sum up omega * MEsq
	sumrule_factor = 1.0/((pow(twoPI * iKmax/RefState.L, 2.0) - Chem_Pot
			       + 4.0 * RefState.c_int * RefState.N/RefState.L)/RefState.L);
      }
      else if (whichDSF == 'q') sumrule_factor = 1.0;
      else if (whichDSF == 'B') sumrule_factor = 1.0;
      else if (whichDSF == 'C') sumrule_factor = 1.0;
      else ABACUSerror("whichDSF option not consistent in Sumrule_Factor");
    }

    return(sumrule_factor);
  }

  void Evaluate_F_Sumrule (char whichDSF, const LiebLin_Bethe_State& RefState, DP Chem_Pot,
			   int iKmin, int iKmax, const char* RAW_Cstr, const char* FSR_Cstr)
  {

    ifstream infile;
    infile.open(RAW_Cstr);
    if(infile.fail()) {
      cout << "Filename RAW_Cstr = " << RAW_Cstr << endl;
      ABACUSerror("Could not open input file in Evaluate_F_Sumrule(LiebLin...).");
    }

    // We run through the data file to check the f sumrule at each positive momenta:
    Vect_DP Sum_omega_MEsq (0.0, iKmax - iKmin + 1);
    Vect_DP Sum_abs_omega_MEsq (0.0, iKmax - iKmin + 1);

    DP Sum_MEsq = 0.0;

    DP omega, ME;
    int iK;
    DP dev;
    string label;
    int nr, nl;

    int nraw = 0;

    while (infile.peek() != EOF) {
      nraw++;
      infile >> omega >> iK >> ME >> dev >> label;
      if (whichDSF == '1') infile >> nr >> nl;
      if (iK >= iKmin && iK <= iKmax) Sum_omega_MEsq[iK - iKmin] += omega * ME * ME;
      if (iK >= iKmin && iK <= iKmax) Sum_abs_omega_MEsq[iK - iKmin] += fabs(omega * ME * ME);
      Sum_MEsq += ME * ME;
    }

    infile.close();

    ofstream outfile;
    outfile.open(FSR_Cstr);
    outfile.precision(16);

    if (whichDSF == 'd' || whichDSF == '1') {

      for (int i = iKmin; i <= iKmax; ++i) {

	if (i > iKmin) outfile << endl;

	outfile << i << "\t" << Sum_omega_MEsq[i - iKmin] * pow(RefState.L, 4.0)
	  /(pow(2.0 * PI * ABACUS::max(abs(i), 1), 2.0) * RefState.N)
	  // Include average of result at +iK and -iK in a third column: iK is at index index(iK) = iK - iKmin
	  // so -iK is at index index(-iK) = -iK - iKmin
	  // We can only use this index if it is >= 0 and < iKmax - iKmin + 1, otherwise third column is copy of second:
		<< "\t" << ((i + iKmin <= 0 && -i < iKmax + 1) ?
			    0.5 * (Sum_omega_MEsq[i - iKmin] + Sum_omega_MEsq[-i - iKmin])
			    : Sum_omega_MEsq[i - iKmin])
	  * pow(RefState.L, 4.0)/(pow(2.0 * PI * ABACUS::max(abs(i), 1), 2.0) * RefState.N);
      }
    }
    else if (whichDSF == 'g' || whichDSF == 'o') {
      for (int i = iKmin; i <= iKmax; ++i) {
	if (i > iKmin) outfile << endl;
	outfile << i << "\t" << Sum_omega_MEsq[i - iKmin] * RefState.L
	  /((4.0 * PI * PI * i * i)/(RefState.L * RefState.L) - Chem_Pot + 4.0 * RefState.c_int * RefState.N/RefState.L)
		<< "\t" << ((i + iKmin <= 0 && -i < iKmax + 1) ?
			    0.5 * (Sum_omega_MEsq[i - iKmin] + Sum_omega_MEsq[-i - iKmin]) : Sum_omega_MEsq[i - iKmin])
	  * RefState.L/((4.0 * PI * PI * i * i)/(RefState.L * RefState.L) - Chem_Pot + 4.0 * RefState.c_int * RefState.N/RefState.L);
      }
    }

    outfile.close();

  }

  void Evaluate_F_Sumrule (string prefix, char whichDSF, const LiebLin_Bethe_State& RefState,
			   DP Chem_Pot, int iKmin, int iKmax)
  {

    stringstream RAW_stringstream;    string RAW_string;
    RAW_stringstream << prefix << ".raw";
    RAW_string = RAW_stringstream.str();    const char* RAW_Cstr = RAW_string.c_str();

    stringstream FSR_stringstream;    string FSR_string;
    FSR_stringstream << prefix << ".fsr";
    FSR_string = FSR_stringstream.str();    const char* FSR_Cstr = FSR_string.c_str();

    Evaluate_F_Sumrule (whichDSF, RefState, Chem_Pot, iKmin, iKmax, RAW_Cstr, FSR_Cstr);

  }

  // Using diagonal state ensemble:
  void Evaluate_F_Sumrule (char whichDSF, DP c_int, DP L, int N, DP kBT, int nstates_req,
			   DP Chem_Pot, int iKmin, int iKmax, const char* FSR_Cstr)
  {

    // We run through the data file to check the f sumrule at each positive momenta:
    Vect_DP Sum_omega_MEsq (0.0, iKmax - iKmin + 1);

    DP Sum_MEsq = 0.0;

    DP omega, ME;
    int iK;
    DP dev;
    string label;
    int nr, nl;

    // Read the weights from the ensembles file:
    LiebLin_Diagonal_State_Ensemble ensemble;

    stringstream ensfilestrstream;
    ensfilestrstream << "LiebLin_c_int_" << c_int << "_L_" << L << "_N_" << N << "_kBT_" << kBT << ".ens";
    string ensfilestr = ensfilestrstream.str();
    const char* ensfile_Cstr = ensfilestr.c_str();

    ensemble.Load(c_int, L, N, ensfile_Cstr);

    for (int ns = 0; ns < ensemble.nstates; ++ns) {

      // Define the raw input file name:
      stringstream filenameprefix;
      Data_File_Name (filenameprefix, whichDSF, iKmin, iKmax, 0.0, ensemble.state[ns],
		      ensemble.state[ns], ensemble.state[ns].label);
      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 infile;
      infile.open(RAW_Cstr);
      if(infile.fail()) {
	cout << "Filename RAW_Cstr = " << RAW_Cstr << endl;
	ABACUSerror("Could not open input file in Evaluate_F_Sumrule(LiebLin...).");
      }

      while (infile.peek() != EOF) {
	infile >> omega >> iK >> ME >> dev >> label;
	if (whichDSF == '1') infile >> nr >> nl;
	if (iK >= iKmin && iK <= iKmax) Sum_omega_MEsq[iK - iKmin] += ensemble.weight[ns] * omega * ME * ME;
	Sum_MEsq += ensemble.weight[ns] * ME * ME;
      }

      infile.close();
    }

    LiebLin_Bethe_State RefState = ensemble.state[0]; // to use the code below, which comes from earlier Evaluate_F_Sumrule

    ofstream outfile;
    outfile.open(FSR_Cstr);
    outfile.precision(16);

    if (whichDSF == 'd' || whichDSF == '1') {
      for (int i = iKmin; i <= iKmax; ++i) {
	if (i > iKmin) outfile << endl;
	outfile << i << "\t" << Sum_omega_MEsq[i - iKmin] * pow(RefState.L, 4.0)
	  /(pow(2.0 * PI * ABACUS::max(abs(i), 1), 2.0) * RefState.N)
	  // Include average of result at +iK and -iK in a third column: iK is at index index(iK) = iK - iKmin
	  // so -iK is at index index(-iK) = -iK - iKmin
	  // We can only use this index if it is >= 0 and < iKmax - iKmin + 1, otherwise third column is copy of second:
		<< "\t" << ((i + iKmin <= 0 && -i < iKmax + 1) ?
			    0.5 * (Sum_omega_MEsq[i - iKmin] + Sum_omega_MEsq[-i - iKmin])
			    : Sum_omega_MEsq[i - iKmin])
	  * pow(RefState.L, 4.0)/(pow(2.0 * PI * ABACUS::max(abs(i), 1), 2.0) * RefState.N);
      }
    }
    else if (whichDSF == 'g' || whichDSF == 'o') {
      for (int i = iKmin; i <= iKmax; ++i) {
	if (i > iKmin) outfile << endl;
	outfile << i << "\t" << Sum_omega_MEsq[i - iKmin] * RefState.L
	  /((4.0 * PI * PI * i * i)/(RefState.L * RefState.L) - Chem_Pot + 4.0 * RefState.c_int * RefState.N/RefState.L)
		<< "\t" << ((i + iKmin <= 0 && -i < iKmax + 1) ?
			    0.5 * (Sum_omega_MEsq[i - iKmin] + Sum_omega_MEsq[-i - iKmin])
			    : Sum_omega_MEsq[i - iKmin]) * RefState.L
	  /((4.0 * PI * PI * i * i)/(RefState.L * RefState.L) - Chem_Pot + 4.0 * RefState.c_int * RefState.N/RefState.L);
      }
    }

    outfile.close();

  }


} // namespace ABACUS