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Jean-Sébastien Caux
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/*! Type II quasisolitons in Lieb-Liniger: rhoxt
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Purpose:
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Produce the .x, .t and .rhoxt files
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respectively containing the coordinate and time vectors, and the rho(x,t) data matrix
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for (multi-)type II hole wavepackets in Lieb-Liniger.
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It automatically makes use of available hardware concurrency.
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This executable requires Abacus version 2.
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See README for compilation instructions.
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Copyright © Jean-Sébastien Caux, Anahita Sarvi and Cesare Vianello.
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This program is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License for more details.
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You should have received a copy of the GNU Affero General Public License along with this program. If not, see <https://www.gnu.org/licenses/>.
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*/
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import std;
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import abacus;
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class Orchestrator
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{
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public:
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Orchestrator(Real c, Real L, int N,
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int nholes, int width, int offset, std::string protocol,
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int Nx, int Nt, Real tmax)
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: c_(c), L_(L), N_(N)
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, nholes_(nholes), width_(width), offset_(offset), protocol_(protocol)
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, Nx_(Nx), Nt_(Nt), tmax_(tmax)
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, rho_expval_(std::vector<std::vector<Real>>(Nx+1, std::vector<Real>(Nt+1)))
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, x_(std::vector<Real>(Nx+1))
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, t_(std::vector<Real>(Nt+1))
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{
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set_up();
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}
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public:
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Real c_;
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Real L_;
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int N_;
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int nholes_;
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int width_;
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int offset_;
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std::string protocol_;
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int Nx_;
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int Nt_;
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Real tmax_;
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int nr_states_;
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std::vector<std::string> label_;
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std::vector<int> iK_;
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std::vector<Real> E_;
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std::vector<std::complex<Real>> amplitude;
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std::map<std::string, std::map<std::string, std::complex<Real>>> rho_ME_;
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std::vector<std::vector<Real>> rho_expval_;
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std::vector<Real> x_;
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std::vector<Real> t_;
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std::queue<int> ix_queue_;
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std::mutex ix_mutex_;
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std::mutex rho_mutex_;
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void set_up();
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void worker();
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void save();
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};
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void Orchestrator::set_up()
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{
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for (int i { 0 }; i <= Nx_; ++i) ix_queue_.push(i);
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// Define the input files
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std::stringstream filename_base;
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filename_base << "c_" << c_ << "_N_" << N_ << "_L_" << L_
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<< "_nholes_" << nholes_ << "_width_" << width_ << "_offset_" << offset_;
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std::stringstream states_filename;
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states_filename << filename_base.str() << ".states";
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std::ifstream states_file;
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states_file.open(states_filename.str());
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states_file >> std::setprecision(std::numeric_limits<Real>::digits10 + 1);
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std::stringstream amplitudes_filename;
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amplitudes_filename << filename_base.str() << "_" << protocol_ << ".amplitudes";
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std::ifstream amplitudes_file;
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amplitudes_file.open(amplitudes_filename.str());
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amplitudes_file >> std::setprecision(std::numeric_limits<Real>::digits10 + 1);
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std::stringstream rho_ME_filename;
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rho_ME_filename << filename_base.str() << ".rho";
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std::ifstream rho_ME_file;
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rho_ME_file.open(rho_ME_filename.str());
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rho_ME_file >> std::setprecision(std::numeric_limits<Real>::digits10 + 1);
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// Input the states info
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std::string tmp_label;
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int tmp_iK;
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Real tmp_E;
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states_file >> tmp_label;
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do {
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states_file >> tmp_iK >> tmp_E;
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label_.push_back(tmp_label);
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iK_.push_back(tmp_iK);
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E_.push_back(tmp_E);
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} while (states_file >> tmp_label);
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states_file.close();
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nr_states_ = int(label_.size());
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// Input the amplitudes
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std::complex<Real> tmp_amplitude;
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for (int is { 0 }; is < nr_states_; ++is) {
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amplitudes_file >> tmp_amplitude;
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amplitude.push_back(tmp_amplitude);
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}
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amplitudes_file.close();
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// Input the density operator matrix elements
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for (int ibra { 0 }; ibra < nr_states_; ++ibra) {
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for (int iket { 0 }; iket <= ibra; ++iket) {
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rho_ME_file >> rho_ME_[label_[ibra]][label_[iket]];
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}
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}
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rho_ME_file.close();
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// Define the output files
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std::stringstream x_filename;
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x_filename << filename_base.str() << "_" << protocol_
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<< "_Nx_" << Nx_ << "_Nt_" << Nt_ << "_tmax_" << tmax_ << ".x";
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std::ofstream x_file;
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x_file.open(x_filename.str(), std::ios::out | std::ios::trunc);
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x_file << std::setprecision(std::numeric_limits<Real>::digits10 + 1);
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std::stringstream t_filename;
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t_filename << filename_base.str() << "_" << protocol_
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<< "_Nx_" << Nx_ << "_Nt_" << Nt_ << "_tmax_" << tmax_ << ".t";
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std::ofstream t_file;
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t_file.open(t_filename.str(), std::ios::out | std::ios::trunc);
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t_file << std::setprecision(std::numeric_limits<Real>::digits10 + 1);
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// Density as function of space and time
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for (int ix { 0 }; ix <= Nx_; ++ix) {
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x_[ix] = -L_/2 + L_ * ix/Nx_;
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x_file << std::endl << -L_/2 + L_ * ix/Nx_;
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}
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x_file.close();
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for (int it { 0 }; it <= Nt_; ++it) {
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t_[it] = tmax_ * it/Nt_;
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t_file << std::endl << tmax_ * it/Nt_;
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}
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t_file.close();
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}
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void Orchestrator::save()
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{
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std::stringstream filename_base;
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filename_base << "c_" << c_ << "_N_" << N_ << "_L_" << L_ << "_nholes_" << nholes_;
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filename_base << "_width_" << width_;
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filename_base << "_offset_" << offset_;
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std::stringstream rhoxt_filename;
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rhoxt_filename << filename_base.str() << "_" << protocol_
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<< "_Nx_" << Nx_ << "_Nt_" << Nt_ << "_tmax_" << tmax_ << ".rhoxt";
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std::ofstream rhoxt_file;
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rhoxt_file.open(rhoxt_filename.str(), std::ios::out | std::ios::trunc);
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rhoxt_file << std::setprecision(std::numeric_limits<Real>::digits10 + 1);
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for (int ix { 0 }; ix <= Nx_; ++ix) {
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for (IndexU it { 0 }; it <= IndexU(Nt_); ++it) {
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rhoxt_file << rho_expval_[ix][it] << "\t";
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}
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rhoxt_file << std::endl;
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}
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rhoxt_file.close();
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}
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void Orchestrator::worker ()
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{
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while (!ix_queue_.empty()) {
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ix_mutex_.lock();
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int ix_here { ix_queue_.front() };
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ix_queue_.pop();
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ix_mutex_.unlock();
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std::vector<Real> computed_rho_expval;
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for (int it { 0 }; it < t_.size(); ++it) {
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Real rho_value { 0 };
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for (int ibra { 0 }; ibra < nr_states_; ++ibra) {
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for (int iket { 0 }; iket < ibra; ++iket) {
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// first add off-diagonal values
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rho_value +=
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2*std::real(std::conj(amplitude[ibra]) * amplitude[iket]
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* rho_ME_[label_[ibra]][label_[iket]]
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* std::exp(1_ir * ((E_[ibra] - E_[iket]) * t_[it] -
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(twopi_r * (iK_[ibra] - iK_[iket]) * x_[ix_here]/L_))));
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}
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// then diagonal one (no factor of 2 here)
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rho_value += std::norm(amplitude[ibra]) * std::real(rho_ME_[label_[ibra]][label_[ibra]]);
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}
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computed_rho_expval.push_back(rho_value);
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}
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rho_mutex_.lock();
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rho_expval_[ix_here].swap(computed_rho_expval);
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rho_mutex_.unlock();
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}
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}
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int main(int argc, char* argv[])
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{
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using namespace std::complex_literals;
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if (argc != 11) {
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std::cout << "Executable rhoxt\n"
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<< " part of the Type II quasisolitons in Lieb-Liniger software suite\n"
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<< " copyright © Jean-Sébastien Caux, Anahita Sarvi and Cesare Vianello.\n";
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std::cout << "\nPurpose:\n"
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<< " Produce the .x, .t and .rhoxt files\n"
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<< " respectively containing the coordinate and time vectors, and the rho(x,t) data matrix\n"
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<< " for (multi-)type II hole wavepackets in Lieb-Liniger.\n";
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std::cout << "\nPrerequirements:\n----------------\n"
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<< " - .states and .rho files produced by executable rho\n"
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<< " - .amplitudes file for the required protocol, produced by executable amplitudes_[protocol type]\n";
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std::cout << "\nUsage:\n------\n";
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std::cout << "rhoxt <c> <L> <N> <nr holes> <width> <offset> <protocol> <Nx> <Nt> <tmax>\n\n";
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int warg { 16 }, wtype { 10 }, wcons { 32 };
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std::cout << std::left << std::setw(warg) << "Argument" << std::setw(wtype) << "Type"
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<< std::setw(wcons) << "Constraints" << "Description\n";
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std::cout << std::left << std::setw(warg) << "--------" << std::setw(wtype) << "----"
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<< std::setw(wcons) << "-----------" << "-----------\n";
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std::cout << std::left << std::setw(warg) << "c" << std::setw(wtype) << "Real"
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<< std::setw(wcons) << "> 0"
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<< "Value of the interaction parameter\n";
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std::cout << std::left << std::setw(warg) << "L" << std::setw(wtype) << "Real"
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<< std::setw(wcons) << "> 0"
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<< "System size\n";
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std::cout << std::left << std::setw(warg) << "N" << std::setw(wtype) << "int"
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<< std::setw(wcons) << "> 0"
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<< "Number of particles\n";
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std::cout << std::left << std::setw(warg) << "nr holes" << std::setw(wtype) << "int"
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<< std::setw(wcons) << "1 <= nr holes <= N"
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<< "Number of holes (Type II modes)\n";
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std::cout << std::left << std::setw(warg) << "width" << std::setw(wtype) << "int"
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<< std::setw(wcons) << "nr holes < width <= N"
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<< "Width of the hole window\n";
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std::cout << std::left << std::setw(warg) << "offset" << std::setw(wtype) << "int"
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<< std::setw(wcons) << "0 <= offset <= N-width"
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<< "Offset of the hole window w/r to the right Fermi edge\n";
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std::cout << std::left << std::setw(warg) << "protocol" << std::setw(wtype) << "string"
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<< std::setw(wcons) << "(see amplitudes executables)"
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<< "Protocol used for defining the amplitudes in the wavepacket\n";
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std::cout << std::left << std::setw(warg) << "Nx" << std::setw(wtype) << "int"
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<< std::setw(wcons) << "> 0"
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<< "Number of spatial sampling points\n";
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std::cout << std::left << std::setw(warg) << "Nt" << std::setw(wtype) << "int"
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<< std::setw(wcons) << "> 0"
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<< "Number of time slices\n";
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std::cout << std::left << std::setw(warg) << "tmax" << std::setw(wtype) << "Real"
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<< std::setw(wcons) << "> 0"
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<< "Maximal time to reach\n";
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return 0;
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}
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std::cout << std::setprecision(std::numeric_limits<Real>::digits10 + 1);
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Real c { std::stold(argv[1]) };
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Real L { std::stold(argv[2]) };
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int N { std::stoi(argv[3]) };
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int nholes { std::stoi(argv[4]) };
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int width { std::stoi(argv[5]) };
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int offset { std::stoi(argv[6]) };
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std::string protocol { argv[7] }; // protocol used to define the amplitudes
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int Nx { std::stoi(argv[8]) }; // number of points for x axis
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int Nt { std::stoi(argv[9]) }; // number of points for t slices
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Real tmax { std::stold(argv[10]) }; // time up to which movie is produced
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Orchestrator orchestrator(c, L, N, nholes, width, offset, protocol, Nx, Nt, tmax);
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int nr_threads_used { ι(std::thread::hardware_concurrency()*2/3) + 1 };
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std::vector<std::thread> threads;
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for (int i { 0 }; i < nr_threads_used; ++i)
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threads.emplace_back(&Orchestrator::worker, &orchestrator);
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for (auto& t : threads) t.join();
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orchestrator.save();
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return 0;
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}
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