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detsdwopdim.cpp
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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. See the enclosed file LICENSE for a copy or if
* that was not distributed with this file, You can obtain one at
* http://mozilla.org/MPL/2.0/.
*
* Copyright 2017 Max H. Gerlach
*
* */
/*
* detsdwopdim.cpp
*
* Created on: Aug 04, 2014
* Author: gerlach
*/
#include <cmath>
#include <numeric>
#include <functional>
#include <array>
#include <tuple>
#include <cassert>
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wpragmas"
#pragma GCC diagnostic ignored "-Wconversion"
#pragma GCC diagnostic ignored "-Wshadow"
#pragma GCC diagnostic ignored "-Wunused-local-typedefs"
#pragma GCC diagnostic ignored "-Wunused-variable"
#include "boost/assign/std/vector.hpp" // 'operator+=()' for vectors
#include "boost/archive/binary_oarchive.hpp"
#include "boost/archive/binary_iarchive.hpp"
#include "boost/iostreams/stream.hpp"
#include "boost/iostreams/device/back_inserter.hpp"
#include "boost/iostreams/device/array.hpp"
#include "boost/filesystem.hpp"
#pragma GCC diagnostic pop
#include "observable.h"
#include "detsdwopdim.h"
#include "exceptions.h"
#include "timing.h"
#include "checkarray.h"
#include "tools.h"
#include "toolsdebug.h"
#include "pytools.h"
namespace fs = boost::filesystem;
template<CheckerboardMethod CBM, int OPDIM>
void createReplica(std::unique_ptr<DetSDW<CBM, OPDIM>>& replica_out,
RngWrapper& rng, ModelParamsDetSDW pars,
DetModelLoggingParams loggingPars /*def arg*/,
const std::string& logfiledir_ /*def arg*/) {
pars = updateTemperatureParameters(pars);
pars.check();
std::string logfiledir = ((logfiledir_ != "") ? logfiledir_ : "./");
loggingPars.logSV_filename = (fs::path(logfiledir) /
fs::path("sv.log")).string();
loggingPars.logSV_max_filename = (fs::path(logfiledir) /
fs::path("svmax.log")).string();
loggingPars.logSV_min_filename = (fs::path(logfiledir) /
fs::path("svmin.log")).string();
loggingPars.logDetRatio_filename = (fs::path(logfiledir) /
fs::path("detratio.log")).string();
loggingPars.logGreen_filename = (fs::path(logfiledir) /
fs::path("green.log")).string();
loggingPars.check();
assert((pars.checkerboard and (CBM == CB_ASSAAD_BERG)) or
(not pars.checkerboard and (CBM == CB_NONE))
);
assert(pars.opdim == OPDIM);
// Update chemical potential setting -- if mux and muy are given, they supersede mu
if (not (pars.specified.count("mux") and pars.specified.count("muy"))) {
pars.mux = pars.mu;
pars.muy = pars.mu;
}
replica_out = std::unique_ptr<DetSDW<CBM, OPDIM>>(
new DetSDW<CBM, OPDIM>(rng, pars, loggingPars, logfiledir));
}
//explicit instantiations:
#ifndef DETSDW_NO_O1
template void createReplica(std::unique_ptr<DetSDW<CB_NONE, 1>>& replica_out,
RngWrapper& rng, ModelParamsDetSDW pars,
DetModelLoggingParams loggingPars /*def arg*/,
const std::string& logfiledir);
template void createReplica(std::unique_ptr<DetSDW<CB_ASSAAD_BERG, 1>>& replica_out,
RngWrapper& rng, ModelParamsDetSDW pars,
DetModelLoggingParams loggingPars /*def arg*/,
const std::string& logfiledir);
#endif //DETSDW_NO_O1
#ifndef DETSDW_NO_O2
template void createReplica(std::unique_ptr<DetSDW<CB_NONE, 2>>& replica_out,
RngWrapper& rng, ModelParamsDetSDW pars,
DetModelLoggingParams loggingPars /*def arg*/,
const std::string& logfiledir);
template void createReplica(std::unique_ptr<DetSDW<CB_ASSAAD_BERG, 2>>& replica_out,
RngWrapper& rng, ModelParamsDetSDW pars,
DetModelLoggingParams loggingPars /*def arg*/,
const std::string& logfiledir);
#endif //DETSDW_NO_O2
#ifndef DETSDW_NO_O3
template void createReplica(std::unique_ptr<DetSDW<CB_NONE, 3>>& replica_out,
RngWrapper& rng, ModelParamsDetSDW pars,
DetModelLoggingParams loggingPars /*def arg*/,
const std::string& logfiledir);
template void createReplica(std::unique_ptr<DetSDW<CB_ASSAAD_BERG, 3>>& replica_out,
RngWrapper& rng, ModelParamsDetSDW pars,
DetModelLoggingParams loggingPars /*def arg*/,
const std::string& logfiledir);
#endif //DETSDW_NO_O3
// define these constants, values are set in the header file
#if __GNUC__ == 4 && __GNUC_MINOR < 7
//work around g++ bug
#define const
#endif// __GNUC__ == 4 && __GNUC_MINOR < 7
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::InitialPhiDelta;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::InitialAngleDelta;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::InitialScaleDelta;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::MinScaleDelta;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::MaxScaleDelta;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::MinAngleDelta;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::MaxAngleDelta;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const uint32_t DetSDW<Checkerboard, OPDIM>::AdjustmentData::AccRatioAdjustmentSamples;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::phiDeltaGrowFactor;
template<CheckerboardMethod Checkerboard, int OPDIM>
constexpr const num DetSDW<Checkerboard, OPDIM>::AdjustmentData::phiDeltaShrinkFactor;
#if __GNUC__ == 4 && __GNUC_MINOR < 7
//work around g++ bug
#undef const
#endif// __GNUC__ == 4 && __GNUC_MINOR < 7
//initial values for field components chosen from this range:
const num PhiLow = -1;
const num PhiHigh = 1;
template<CheckerboardMethod CB, int OPDIM>
DetSDW<CB, OPDIM>::DetSDW(RngWrapper& rng_, const ModelParams& pars_,
const DetModelLoggingParams& loggingPars /*def arg*/,
const std::string& logfiledir_ /*def arg*/) :
Base(pars_, (pars_.turnoffFermions ? 1 // save memory in no fermion case
: (MatrixSizeFactor * pars_.L*pars_.L)),
loggingPars),
smalleye(arma::eye<MatData>(MatrixSizeFactor, MatrixSizeFactor)),
rng(rng_), normal_distribution(rng),
pars(pars_),
us(), // UpdateStatistics
hopHor(), hopVer(), sinhHopHor(), sinhHopVer(), coshHopHor(), coshHopVer(),
sinhHopHorHalf(), sinhHopVerHalf(), coshHopHorHalf(), coshHopVerHalf(),
mu(),
spaceNeigh(pars.L), timeNeigh(pars.m),
propK(), propKx(propK[XBAND]), propKy(propK[YBAND]),
propK_half(), propKx_half(propK_half[XBAND]), propKy_half(propK_half[YBAND]),
propK_half_inv(), propKx_half_inv(propK_half_inv[XBAND]), propKy_half_inv(propK_half_inv[YBAND]),
g(green[0]), g_inv_sv(green_inv_sv[0]),
phi(pars.N, OPDIM, pars.m+1), cdwl(pars.N, pars.m+1),
coshTermPhi(pars.N, pars.m+1), sinhTermPhi(pars.N, pars.m+1),
coshTermCDWl(pars.N, pars.m+1), sinhTermCDWl(pars.N, pars.m+1),
ad(pars), // AdjustmentData
performedSweeps(0),
meanPhi(), normMeanPhi(0), phiRhoS_Gs(0), phiRhoS_Gc(0),
associatedEnergy(0),
// kgreenXUP(), kgreenYDOWN(), kgreenXDOWN(), kgreenYUP(),
greenXUPXUP_summed(), greenYDOWNYDOWN_summed(), greenXDOWNXDOWN_summed(), greenYUPYUP_summed(),
greenXUPYDOWN_summed(), greenYDOWNXUP_summed(),
greenK0(), greenLocal(),
kOcc(), kOccX(kOcc[XBAND]), kOccY(kOcc[YBAND]),
// occ(), occX(occ[XBAND]), occY(occ[YBAND]),
pairPlusMax(0.0), pairMinusMax(0.0),
pairPlus(), pairMinus(),
fermionEkinetic(0), fermionEcouple(0),
// occCorr(), chargeCorr(), occCorrFT(), chargeCorrFT(), occDiffSq(),
timeslices_included_in_measurement(),
dud(pars.N, pars.delaySteps), gmd(pars.N, m, pars_.turnoffFermions),
greenConsistencyLogger(logfiledir_, loggingPars.logGreenConsistency), detRatioLogging(), greenLogging()
{
//use contents of ModelParams pars
assert((pars.checkerboard and CB != CB_NONE) or (not pars.checkerboard and CB == CB_NONE));
assert(pars.N == pars.L*pars.L);
assert(pars.d == 2);
//zero some dynamic data
phi.zeros();
// std::cout << phi;
cdwl.zeros();
coshTermPhi.zeros();
sinhTermPhi.zeros();
coshTermCDWl.ones();
sinhTermCDWl.zeros();
if (not pars.phiFixed) {
setupRandomField();
} else {
setupConstantField();
}
//weak magnetic field in z-direction
if (pars.weakZflux) {
zmag[XUP] = +1.0 / (pars.N);
zmag[YDOWN] = +1.0 / (pars.N);
zmag[YUP] = -1.0 / (pars.N);
zmag[XDOWN] = -1.0 / (pars.N);
} else {
zmag[XUP] = 0.0;
zmag[YDOWN] = 0.0;
zmag[YUP] = 0.0;
zmag[XDOWN] = 0.0;
}
//hopping constants. These are the t_ij in sum_<i,j> -t_ij c^+_i c_j
//So for actual calculations an additional minus-sign needs to be included.
//In the case of anti-periodic boundaries between i and j, another extra minus-sign
//must be added.
hopHor[XBAND] = pars.txhor;
hopVer[XBAND] = pars.txver;
hopHor[YBAND] = pars.tyhor;
hopVer[YBAND] = pars.tyver;
//precalculate hyperbolic functions, used in checkerboard decomposition [without magnetic field]
using std::sinh; using std::cosh;
num dtauHere = pars.dtau; // to fix capture issues
for_each_band( [this, dtauHere](Band band) {
sinhHopHor[band] = sinh(-dtauHere * hopHor[band]);
coshHopHor[band] = cosh(-dtauHere * hopHor[band]);
sinhHopVer[band] = sinh(-dtauHere * hopVer[band]);
coshHopVer[band] = cosh(-dtauHere * hopVer[band]);
sinhHopHorHalf[band] = sinh(-0.5*dtauHere * hopHor[band]);
coshHopHorHalf[band] = cosh(-0.5*dtauHere * hopHor[band]);
sinhHopVerHalf[band] = sinh(-0.5*dtauHere * hopVer[band]);
coshHopVerHalf[band] = cosh(-0.5*dtauHere * hopVer[band]);
} );
if (pars.weakZflux) {
// needed for checkerboard computations when we have a magnetic field
precalc_4site_hopping_exponentials();
}
//chemical potential
//These are the \mu in sum_<i> -\mu c^+_i c_i
//So for actual calculations an additional minus-sign needs to be included.
mu[XBAND] = pars.mux;
mu[YBAND] = pars.muy;
if (not pars.turnoffFermions) {
setupPropK();
}
setupUdVStorage_and_calculateGreen();
using std::cref;
using namespace boost::assign;
obsScalar += ScalarObservable(cref(normMeanPhi), "normMeanPhi", "nmp"),
ScalarObservable(cref(associatedEnergy), "associatedEnergy", "");
if (OPDIM == 2) {
obsScalar += ScalarObservable(cref(phiRhoS_Gs), "phiRhoS_Gs", "");
obsScalar += ScalarObservable(cref(phiRhoS_Gc), "phiRhoS_Gc", "");
}
if (not (pars.turnoffFermions or pars.turnoffFermionMeasurements)) {
obsScalar +=
ScalarObservable(cref(pairPlusMax), "pairPlusMax", "ppMax"),
ScalarObservable(cref(pairMinusMax), "pairMinusMax", "pmMax")// ,
// ScalarObservable(cref(fermionEkinetic), "fermionEkinetic", "fEkin"),
// ScalarObservable(cref(fermionEcouple), "fermionEcouple", "fEcouple")
;
kOccX.zeros(pars.N);
kOccY.zeros(pars.N);
obsVector += VectorObservable(cref(kOccX), pars.N, "kOccX", "nkx"),
VectorObservable(cref(kOccY), pars.N, "kOccY", "nky");
// output some different sectors of the Green's function in the
// momentum space representation
// obsVector += VectorObservable(cref(kgreenXUP), pars.N, "kgreenXUP", ""),
// VectorObservable(cref(kgreenYDOWN), pars.N, "kgreenYDOWN", ""),
// VectorObservable(cref(kgreenXUP), pars.N, "kgreenXUP", ""),
// VectorObservable(cref(kgreenYDOWN), pars.N, "kgreenYDOWN", "");
// kgreenXUP.zeros(pars.N);
// kgreenYDOWN.zeros(pars.N);
// kgreenXDOWN.zeros(pars.N);
// kgreenYUP.zeros(pars.N);
obsScalar += ScalarObservable(cref(greenK0), "greenK0", ""),
ScalarObservable(cref(greenLocal), "greenLocal", "");
// occX.zeros(pars.N);
// occY.zeros(pars.N);
// obsVector += VectorObservable(cref(occX), pars.N, "occX", "nx"),
// VectorObservable(cref(occY), pars.N, "occY", "ny");
//attention:
// these do not have valid entries for site 0
pairPlus.zeros(pars.N);
pairMinus.zeros(pars.N);
obsVector += VectorObservable(cref(pairPlus), pars.N, "pairPlus", "pp"),
VectorObservable(cref(pairMinus), pars.N, "pairMinus", "pm");
// const Band BandValues[2] = {XBAND, YBAND};
// for (Band b1 : BandValues) {
// for (Band b2 : BandValues) {
// MatNum& occC = occCorr(b1, b2);
// occC.zeros(pars.N,pars.N);
// VecNum& occCFT = occCorrFT(b1, b2);
// occCFT.zeros(pars.N);
// obsVector += VectorObservable(cref(occCFT), pars.N, "occCorrFT" + bandstr(b1) + bandstr(b2), "");
// }
// }
// chargeCorr.zeros(pars.N,pars.N);
// chargeCorrFT.zeros(pars.N);
// obsVector += VectorObservable(cref(chargeCorrFT), pars.N, "chargeCorrFT", "");
occDiffSq = 0.0;
obsScalar += ScalarObservable(cref(occDiffSq), "occDiffSq", "");
}
consistencyCheck();
// for consistency checks:
if (loggingParams.checkAndLogDetRatio) {
detRatioLogging = std::unique_ptr<DoubleVectorWriterSuccessive>(
new DoubleVectorWriterSuccessive(
loggingParams.logDetRatio_filename,
false // append to file = false: always start a new file for this
)
);
detRatioLogging->addHeaderText("Attention: this file is recreated and the log restarted for each run of the program. It is not continued if the simulation is resumed from a saved state.");
detRatioLogging->addHeaderText("Here we log the difference of two possible evaluations of the Green's function determinant ratio");
detRatioLogging->writeHeader();
}
if (loggingParams.checkAndLogGreen) {
greenLogging = std::unique_ptr<DoubleVectorWriterSuccessive>(
new DoubleVectorWriterSuccessive(
loggingParams.logGreen_filename,
false // append to file = false: always start a new file for this
)
);
greenLogging->addHeaderText("Attention: this file is recreated and the log restarted for each run of the program. It is not continued if the simulation is resumed from a saved state.");
greenLogging->addHeaderText("Here we log the maximum absolute difference of two possible evaluations of the updated Green's function");
greenLogging->writeHeader();
}
}
template<CheckerboardMethod CB, int OPDIM>
void DetSDW<CB, OPDIM>::setupUdVStorage_and_calculateGreen() {
if (not pars.turnoffFermions) {
//setupUdVStorage_and_calculateGreen_skeleton(sdwComputeBmat(this));
setupUdVStorage_and_calculateGreen_skeleton(sdwLeftMultiplyBmat(this));
} else {
g.zeros();
}
}
template<CheckerboardMethod CB, int OPDIM>
void DetSDW<CB, OPDIM>::setupUdVStorage_and_calculateGreen_forTimeslice(
uint32_t timeslice) {
if (not pars.turnoffFermions) {
//setupUdVStorage_and_calculateGreen_skeleton(sdwComputeBmat(this));
setupUdVStorage_and_calculateGreen_forTimeslice_skeleton(
timeslice, sdwLeftMultiplyBmat(this));
} else {
g.zeros();
}
}
template<CheckerboardMethod CB, int OPDIM>
DetSDW<CB, OPDIM>::~DetSDW() {
}
template<CheckerboardMethod CB, int OPDIM>
uint32_t DetSDW<CB, OPDIM>::getSystemN() const {
return pars.N;
}
template<CheckerboardMethod CB, int OPDIM>
MetadataMap DetSDW<CB, OPDIM>::prepareModelMetadataMap() const {
MetadataMap meta = pars.prepareMetadataMap();
#define META_INSERT(VAR) {meta[#VAR] = numToString(VAR);}
if (pars.globalShift) {
num globalShiftAccRatio = 0.;
if (us.attemptedGlobalShifts > 0) {
globalShiftAccRatio =
num(us.acceptedGlobalShifts) / num(us.attemptedGlobalShifts);
}
META_INSERT(globalShiftAccRatio);
}
if (pars.wolffClusterUpdate) {
num wolffClusterUpdateAccRatio = 0.0;
if (us.attemptedWolffClusterUpdates) {
wolffClusterUpdateAccRatio =
num(us.acceptedWolffClusterUpdates) /
num(us.attemptedWolffClusterUpdates);
}
META_INSERT(wolffClusterUpdateAccRatio);
num averageAcceptedWolffClusterSize = 0.0;
if (us.acceptedWolffClusterUpdates) {
averageAcceptedWolffClusterSize =
us.addedWolffClusterSize / num(us.acceptedWolffClusterUpdates);
}
META_INSERT(averageAcceptedWolffClusterSize);
}
if (pars.wolffClusterShiftUpdate) {
num wolffClusterShiftUpdateAccRatio = 0.;
if (us.attemptedWolffClusterShiftUpdates) {
wolffClusterShiftUpdateAccRatio =
num(us.acceptedWolffClusterShiftUpdates) /
num(us.attemptedWolffClusterShiftUpdates);
}
META_INSERT(wolffClusterShiftUpdateAccRatio);
num averageAcceptedWolffClusterSize = 0.;
if (us.acceptedWolffClusterShiftUpdates) {
averageAcceptedWolffClusterSize =
us.addedWolffClusterSize / num(us.acceptedWolffClusterShiftUpdates);
}
META_INSERT(averageAcceptedWolffClusterSize);
}
#undef META_INSERT
return meta;
}
template<CheckerboardMethod CB, int OPDIM>
void DetSDW<CB, OPDIM>::initMeasurements() {
timing.start("sdw-measure");
timeslices_included_in_measurement.clear();
//meanPhi
meanPhi.zeros();
normMeanPhi = 0;
// bosonic spin stiffness
if (OPDIM == 2) {
phiRhoS_Gs = 0.0;
phiRhoS_Gc = 0.0;
}
associatedEnergy = 0;
if (not (pars.turnoffFermions or pars.turnoffFermionMeasurements)) {
if (pars.dumpGreensFunction) {
// some sectors of the momentum space Green's function,
// helpers:
greenXUPXUP_summed.zeros(pars.N, pars.N);
greenYDOWNYDOWN_summed.zeros(pars.N, pars.N);
if (OPDIM == 3) {
greenXDOWNXDOWN_summed.zeros(pars.N, pars.N);
greenYUPYUP_summed.zeros(pars.N, pars.N);
}
greenXUPYDOWN_summed.zeros(pars.N, pars.N);
greenYDOWNXUP_summed.zeros(pars.N, pars.N);
}
// scalar functions of the Green's function
greenK0 = 0.;
greenLocal = 0.;
// //fermion occupation number -- real space
// occX.zeros(pars.N);
// occY.zeros(pars.N);
//fermion occupation number -- k-space
kOccX.zeros(pars.N);
kOccY.zeros(pars.N);
//equal-time pairing-correlations
pairPlus.zeros(pars.N);
pairMinus.zeros(pars.N);
// // Fermionic energy contribution
// fermionEkinetic = 0;
// fermionEcouple = 0;
// // band occupation / charge correlations
// const Band BandValues[2] = {XBAND, YBAND};
// for (Band b1 : BandValues) {
// for (Band b2 : BandValues) {
// MatNum& occC = occCorr(b1, b2);
// occC.zeros(pars.N,pars.N);
// }
// }
occDiffSq = 0.0;
}
timing.stop("sdw-measure");
}
template<CheckerboardMethod CB, int OPDIM>
void DetSDW<CB, OPDIM>::measure(uint32_t timeslice) {
// This function *adds* the measurements for the current timeslice
// to the observable variable, which must have been zero'ed in
// initMeasurements. Then finishMeasurements() will divide the
// observable variable to get the average over all timeslices.
timing.start("sdw-measure");
// to ease notation in here
const auto L = pars.L;
const auto N = pars.N;
timeslices_included_in_measurement.insert(timeslice);
// bosonic spin stiffness
if (OPDIM == 2) {
for (uint32_t site = 0; site < N; ++site) {
Phi phi_site = getPhi(site, timeslice);
Phi phi_xneigh = getPhi(spaceNeigh(XPLUS, site), timeslice);
Phi phi_yneigh = getPhi(spaceNeigh(YPLUS, site), timeslice);
phiRhoS_Gc += arma::dot(phi_site, phi_xneigh) +
arma::dot(phi_site, phi_yneigh);
phiRhoS_Gs += phi_xneigh[0] * phi_site[1] -
phi_xneigh[1] * phi_site[0];
}
}
//normphi, meanPhi, sdw-susceptibility, associatedEnergy
for (uint32_t site = 0; site < pars.N; ++site) {
Phi phi_site = getPhi(site, timeslice);
meanPhi += phi_site;
associatedEnergy += arma::dot(phi_site, phi_site);
}
if (not (pars.turnoffFermions or pars.turnoffFermionMeasurements)) {
MatData gshifted = shiftGreenSymmetric();
// some sectors of the momentum space Green's function
// helpers:
auto gblock = [&gshifted, N](uint32_t row, uint32_t col) {
return gshifted.submat(row * N, col * N,
(row + 1) * N - 1, (col + 1) * N - 1);
};
if (pars.dumpGreensFunction) {
greenXUPXUP_summed += gblock(0, 0);
greenYDOWNYDOWN_summed += gblock(1, 1);
if (OPDIM == 3) {
greenXDOWNXDOWN_summed += gblock(2, 2);
greenYUPYUP_summed += gblock(3, 3);
}
greenXUPYDOWN_summed += gblock(0, 1);
greenYDOWNXUP_summed += gblock(1, 0);
}
// scalar functions of the Green's function
if (OPDIM == 3) {
greenK0 += std::real(arma::accu( gshifted ));
}
else {
// only the 2x2 top-left and 2x2 bottom-right blocks of G are non-zero
//
// Sum [ Green ] = Sum [ Green_XUP_YDOWN ] + Sum [ Green_XDOWN_YUP ]
// = Sum [ Green_XUP_YDOWN ] + Sum [ Green_XUP_YDOWN^(*) ]
// = 2 * Sum [ Real ( Green_XUP_YDOWN ) ]
greenK0 += 2 * std::real( arma::accu( gshifted ) );
}
if (OPDIM == 3) {
// cpx local_with_imag = arma::trace(gshifted) / (4. * N);
// assert( std::abs(std::imag(local_with_imag)) < 1E-14 );
greenLocal += std::real(arma::trace(gshifted)) / (4. * N);
}
else {
// Trace [ Green ] = Trace [ Green_XUP_YDOWN ] + Trace [ Green_XDOWN_YUP ]
// = Trace [ Green_XUP_YDOWN ] + Trace [ Green_XUP_YDOWN^(*) ]
// = 2 * Trace [ Real ( Green_XUP_YDOWN ) ]
greenLocal += 2. * std::real(arma::trace( gshifted )) / (4. * N);
}
//helper function to access the Green's function elements for the
//current time slice, definition depending on OPDIM
// *1 is for the row index,
// *2 is for the column index
auto gl1 = [this, N, &gshifted](uint32_t site1, BandSpin bs1,
uint32_t site2, BandSpin bs2) -> DataType {
static_assert(XUP == 0, "XUP wrong"); static_assert(YDOWN == 1, "YDOWN wrong");
static_assert(XDOWN == 2, "XDOWN wrong"); static_assert(YUP == 3, "YUP wrong");
if (OPDIM == 3) {
return gshifted(site1 + N*bs1, site2 + N*bs2);
}
else {
if ((bs1 == XUP or bs1 == YDOWN) and (bs2 == XUP or bs2 == YDOWN)) {
return gshifted(site1 + N*bs1, site2 + N*bs2);
}
else if ((bs1 == XDOWN or bs1 == YUP) and (bs2 == XDOWN or bs2 == YUP)) {
return std::conj(gshifted(site1 + N*(bs1-2), site2 + N*(bs2-2)));
}
else {
return DataType(0);
}
}
};
auto gl = [this, N, &gl1](uint32_t site1, Band band1, Spin spin1,
uint32_t site2, Band band2, Spin spin2) -> DataType {
typedef DetSDW<CB,OPDIM> D;
BandSpin bs1 = D::getBandSpin(band1, spin1);
BandSpin bs2 = D::getBandSpin(band2, spin2);
return gl1(site1, bs1, site2, bs2);
};
// //fermion occupation number -- real space
// for (uint32_t i = 0; i < N; ++i) {
// occX[i] += std::real(gl1(i, XUP, i, XUP) + gl1(i, XDOWN, i, XDOWN));
// occY[i] += std::real(gl1(i, YUP, i, YUP) + gl1(i, YDOWN, i, YDOWN));
// }
//fermion occupation number -- k-space
static const num pi = M_PI;
//offset k-components for antiperiodic bc
num offset_x = 0.0;
num offset_y = 0.0;
if (pars.bc == BC_Type::APBC_X or pars.bc == BC_Type::APBC_XY) {
offset_x = 0.5;
}
if (pars.bc == BC_Type::APBC_Y or pars.bc == BC_Type::APBC_XY) {
offset_y = 0.5;
}
for (uint32_t ksite = 0; ksite < N; ++ksite) {
uint32_t ksitey = ksite / L;
uint32_t ksitex = ksite % L;
num ky = -pi + (num(ksitey) + offset_y) * 2*pi / num(L);
num kx = -pi + (num(ksitex) + offset_x) * 2*pi / num(L);
for (uint32_t i = 0; i < N; ++i) {
num iy = num(i / L);
num ix = num(i % L);
for (uint32_t j = 0; j < N; ++j) {
num jy = num(j / L);
num jx = num(j % L);
num argument = kx * (ix - jx) + ky * (iy - jy);
cpx phase = std::exp(cpx(0, argument));
DataType green_x_up = gl1(i, XUP, j, XUP);
DataType green_x_down = gl1(i, XDOWN, j, XDOWN);
DataType green_y_up = gl1(i, YUP, j, YUP);
DataType green_y_down = gl1(i, YDOWN, j, YDOWN);
cpx x_cpx = phase * (green_x_up + green_x_down);
cpx y_cpx = phase * (green_y_up + green_y_down);
kOccX[ksite] += std::real(x_cpx);
kOccY[ksite] += std::real(y_cpx);
}
}
}
//equal-time pairing-correlations
//-------------------------------
for (uint32_t i = 0; i < N; ++i) {
// checkarray<std::tuple<uint32_t,uint32_t>, 2> sitePairs = {
// std::make_tuple(i, 0), std::make_tuple(0, i)
// };
//compiler-compatibilty fix
std::tuple<uint32_t,uint32_t> sitePairs[2] = {
std::tuple<uint32_t,uint32_t>(i, 0),
std::tuple<uint32_t,uint32_t>(0, i)
};
DataType pairPlusCpx(0);
DataType pairMinusCpx(0);
for (auto sites : sitePairs) {
uint32_t siteA = std::get<0>(sites);
uint32_t siteB = std::get<1>(sites);
// the following two unwieldy sums have been evaluated with the Mathematica
// notebook pairing-corr.nb (and they match the terms calculated by hand on paper)
pairPlusCpx += DataType(-4.0) * (
gl(siteA, XBAND, SPINDOWN, siteB, XBAND, SPINUP)*gl(siteA, XBAND, SPINUP, siteB, XBAND, SPINDOWN) -
gl(siteA, XBAND, SPINDOWN, siteB, XBAND, SPINDOWN)*gl(siteA, XBAND, SPINUP, siteB, XBAND, SPINUP) +
gl(siteA, XBAND, SPINDOWN, siteB, YBAND, SPINUP)*gl(siteA, XBAND, SPINUP, siteB, YBAND, SPINDOWN) -
gl(siteA, XBAND, SPINDOWN, siteB, YBAND, SPINDOWN)*gl(siteA, XBAND, SPINUP, siteB, YBAND, SPINUP) +
gl(siteA, YBAND, SPINDOWN, siteB, XBAND, SPINUP)*gl(siteA, YBAND, SPINUP, siteB, XBAND, SPINDOWN) -
gl(siteA, YBAND, SPINDOWN, siteB, XBAND, SPINDOWN)*gl(siteA, YBAND, SPINUP, siteB, XBAND, SPINUP) +
gl(siteA, YBAND, SPINDOWN, siteB, YBAND, SPINUP)*gl(siteA, YBAND, SPINUP, siteB, YBAND, SPINDOWN) -
gl(siteA, YBAND, SPINDOWN, siteB, YBAND, SPINDOWN)*gl(siteA, YBAND, SPINUP, siteB, YBAND, SPINUP)
);
pairMinusCpx += DataType(-4.0) * (
gl(siteA, XBAND, SPINDOWN, siteB, XBAND, SPINUP)*gl(siteA, XBAND, SPINUP, siteB, XBAND, SPINDOWN) -
gl(siteA, XBAND, SPINDOWN, siteB, XBAND, SPINDOWN)*gl(siteA, XBAND, SPINUP, siteB, XBAND, SPINUP) -
gl(siteA, XBAND, SPINDOWN, siteB, YBAND, SPINUP)*gl(siteA, XBAND, SPINUP, siteB, YBAND, SPINDOWN) +
gl(siteA, XBAND, SPINDOWN, siteB, YBAND, SPINDOWN)*gl(siteA, XBAND, SPINUP, siteB, YBAND, SPINUP) -
gl(siteA, YBAND, SPINDOWN, siteB, XBAND, SPINUP)*gl(siteA, YBAND, SPINUP, siteB, XBAND, SPINDOWN) +
gl(siteA, YBAND, SPINDOWN, siteB, XBAND, SPINDOWN)*gl(siteA, YBAND, SPINUP, siteB, XBAND, SPINUP) +
gl(siteA, YBAND, SPINDOWN, siteB, YBAND, SPINUP)*gl(siteA, YBAND, SPINUP, siteB, YBAND, SPINDOWN) -
gl(siteA, YBAND, SPINDOWN, siteB, YBAND, SPINDOWN)*gl(siteA, YBAND, SPINUP, siteB, YBAND, SPINUP)
);
}
pairPlus[i] += std::real(pairPlusCpx);
//pairPlusimag[i] += std::imag(pairPlusCpx);
pairMinus[i] += std::real(pairMinusCpx);
//pairMinusimag[i] += std::imag(pairMinusCpx);
}
// Fermionic energy contribution
// -----------------------------
auto glij = [this, gl](uint32_t site1, uint32_t site2, Band band, Spin spin) -> DataType {
return gl(site1, band, spin,
site2, band, spin);
};
const auto txhor = pars.txhor;
const auto txver = pars.txver;
const auto tyhor = pars.tyhor;
const auto tyver = pars.tyver;
// code using this commented out
(void)glij;
(void)txhor; (void)txver; (void)tyhor; (void)tyver;
// for (uint32_t i = 0; i < N; ++i) {
// //TODO: write in a nicer fashion using hopping-array as used in the checkerboard branch
// Spin spins[] = {SPINUP, SPINDOWN};
// for (auto spin: spins) {
// DataType e = DataType(txhor) * glij(i, spaceNeigh(XPLUS, i), XBAND, spin)
// + DataType(txhor) * glij(i, spaceNeigh(XMINUS,i), XBAND, spin)
// + DataType(txver) * glij(i, spaceNeigh(YPLUS, i), XBAND, spin)
// + DataType(txver) * glij(i, spaceNeigh(YMINUS,i), XBAND, spin)
// + DataType(tyhor) * glij(i, spaceNeigh(XPLUS, i), YBAND, spin)
// + DataType(tyhor) * glij(i, spaceNeigh(XMINUS,i), YBAND, spin)
// + DataType(tyver) * glij(i, spaceNeigh(YPLUS, i), YBAND, spin)
// + DataType(tyver) * glij(i, spaceNeigh(YMINUS,i), YBAND, spin);
// fermionEkinetic += std::real(e);
// //fermionEkinetic_imag += std::imag(e);
// }
// }
// for (uint32_t i = 0; i < N; ++i) {
// auto glbs = [this, i, gl](Band band1, Spin spin1,
// Band band2, Spin spin2) -> DataType {
// return gl(i, band1, spin1, i, band2, spin2);
// };
// //factors for different combinations of spins
// //overall factor of -1 included
// // up_up, up_dn, dn_up, dn_dn;
// DataType up_up(0);
// DataType up_dn = DataType(-phi(i,0,timeslice)); // real part
// DataType dn_up = DataType(-phi(i,0,timeslice));
// DataType dn_dn(0);
// if (OPDIM >= 2) {
// setImag(up_dn, +phi(i,1,timeslice));
// setImag(dn_up, -phi(i,1,timeslice));
// }
// if (OPDIM == 3) {
// up_up = DataType(-phi(i,2,timeslice));
// dn_dn = DataType(+phi(i,2,timeslice));
// }
// DataType e = up_up * (glbs(XBAND, SPINUP, YBAND, SPINUP) +
// glbs(YBAND, SPINUP, XBAND, SPINUP))
// + up_dn * (glbs(XBAND, SPINUP, YBAND, SPINDOWN) +
// glbs(YBAND, SPINUP, XBAND, SPINDOWN))
// + dn_up * (glbs(XBAND, SPINDOWN, YBAND, SPINUP) +
// glbs(YBAND, SPINDOWN, XBAND, SPINUP))
// + dn_dn * (glbs(XBAND, SPINDOWN, YBAND, SPINDOWN) +
// glbs(YBAND, SPINDOWN, XBAND, SPINDOWN));
// fermionEcouple += std::real(e);
// //fermionEcouple_imag += std::imag(e);
// }
// band occupation / charge correlations
// -------------------------------------
// code generated in Mathematica: sdw-cdw-corr-obs.nb
// for (uint32_t i = 0; i < N; ++i) {
// for (uint32_t j = 0; j < N; ++j) {
// if (i != j) {
// //unequal sites, slightly generic
// const Band BandValues[2] = {XBAND, YBAND};
// for (Band b1 : BandValues) {
// for (Band b2 : BandValues) {
// DataType contrib = 4.0 -
// gl(i, b1, SPINDOWN, j, b2, SPINDOWN)*
// gl(j, b2, SPINDOWN, i, b1, SPINDOWN) -
// gl(i, b1, SPINUP, j, b2, SPINDOWN)*
// gl(j, b2, SPINDOWN, i, b1, SPINUP) - 2.0*
// gl(j, b2, SPINDOWN, j, b2, SPINDOWN) -
// gl(i, b1, SPINDOWN, j, b2, SPINUP)*
// gl(j, b2, SPINUP, i, b1, SPINDOWN) -
// gl(i, b1, SPINUP, j, b2, SPINUP)*
// gl(j, b2, SPINUP, i, b1, SPINUP) - 2.0*
// gl(j, b2, SPINUP, j, b2, SPINUP) +
// gl(i, b1, SPINDOWN, i, b1, SPINDOWN)*
// (-2.0 +
// gl(j, b2, SPINDOWN, j, b2, SPINDOWN) +
// gl(j, b2, SPINUP, j, b2, SPINUP)) +
// gl(i, b1, SPINUP, i, b1, SPINUP)*
// (-2.0 +
// gl(j, b2, SPINDOWN, j, b2, SPINDOWN) +
// gl(j, b2, SPINUP, j, b2, SPINUP));
// occCorr(b1, b2)(i, j) += std::real(contrib);
// }
// }
// } else {
// //equal site i, use band-specific code
// DataType contribxx = 4.0 - 2.0*
// gl(i, XBAND, SPINDOWN, i, XBAND, SPINUP)*
// gl(i, XBAND, SPINUP, i, XBAND, SPINDOWN) - 3.0*
// gl(i, XBAND, SPINUP, i, XBAND, SPINUP) +
// gl(i, XBAND, SPINDOWN, i, XBAND, SPINDOWN)*
// (-3.0 + 2.0*
// gl(i, XBAND, SPINUP, i, XBAND, SPINUP));
// occCorr(XBAND,XBAND)(i, i) += std::real(contribxx);
// DataType contribxy = 4.0 -
// gl(i, XBAND, SPINDOWN, i, YBAND, SPINDOWN)*
// gl(i, YBAND, SPINDOWN, i, XBAND, SPINDOWN) -
// gl(i, XBAND, SPINUP, i, YBAND, SPINDOWN)*
// gl(i, YBAND, SPINDOWN, i, XBAND, SPINUP) - 2.0*
// gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN) -
// gl(i, XBAND, SPINDOWN, i, YBAND, SPINUP)*
// gl(i, YBAND, SPINUP, i, XBAND, SPINDOWN) -
// gl(i, XBAND, SPINUP, i, YBAND, SPINUP)*
// gl(i, YBAND, SPINUP, i, XBAND, SPINUP) - 2.0*
// gl(i, YBAND, SPINUP, i, YBAND, SPINUP) +
// gl(i, XBAND, SPINDOWN, i, XBAND, SPINDOWN)*
// (-2.0 +
// gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN) +
// gl(i, YBAND, SPINUP, i, YBAND, SPINUP)) +
// gl(i, XBAND, SPINUP, i, XBAND, SPINUP)*
// (-2.0 +
// gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN) +
// gl(i, YBAND, SPINUP, i, YBAND, SPINUP));
// occCorr(XBAND,YBAND)(i,i) += std::real(contribxy);
// occCorr(YBAND,XBAND)(i,i) += std::real(contribxy); // it's symmetric in xy
// DataType contribyy = 4.0 - 2.0*
// gl(i, YBAND, SPINDOWN, i, YBAND, SPINUP)*
// gl(i, YBAND, SPINUP, i, YBAND, SPINDOWN) - 3.0*
// gl(i, YBAND, SPINUP, i, YBAND, SPINUP) +
// gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN)*
// (-3.0 + 2.0*
// gl(i, YBAND, SPINUP, i, YBAND, SPINUP));
// occCorr(YBAND,YBAND)(i,i) += std::real(contribyy);
// }
// }
// }
DataType occDiffSqContrib = 0.0;
for (uint32_t i = 0; i < N; ++i) {
occDiffSqContrib += -2.0*
gl(i, XBAND, SPINDOWN, i, XBAND, SPINUP)*
gl(i, XBAND, SPINUP, i, XBAND, SPINDOWN) +
gl(i, XBAND, SPINUP, i, XBAND, SPINUP) + 2.0*
gl(i, XBAND, SPINDOWN, i, YBAND, SPINDOWN)*
gl(i, YBAND, SPINDOWN, i, XBAND, SPINDOWN) + 2.0*
gl(i, XBAND, SPINUP, i, YBAND, SPINDOWN)*
gl(i, YBAND, SPINDOWN, i, XBAND, SPINUP) +
gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN) - 2.0*
gl(i, XBAND, SPINUP, i, XBAND, SPINUP)*
gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN) + 2.0*
gl(i, XBAND, SPINDOWN, i, YBAND, SPINUP)*
gl(i, YBAND, SPINUP, i, XBAND, SPINDOWN) + 2.0*
gl(i, XBAND, SPINUP, i, YBAND, SPINUP)*
gl(i, YBAND, SPINUP, i, XBAND, SPINUP) - 2.0*
gl(i, YBAND, SPINDOWN, i, YBAND, SPINUP)*
gl(i, YBAND, SPINUP, i, YBAND, SPINDOWN) +
gl(i, XBAND, SPINDOWN, i, XBAND, SPINDOWN)*
(1.0 + 2.0*
gl(i, XBAND, SPINUP, i, XBAND, SPINUP) - 2.0*
gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN) - 2.0*
gl(i, YBAND, SPINUP, i, YBAND, SPINUP)) +
gl(i, YBAND, SPINUP, i, YBAND, SPINUP) - 2.0*
gl(i, XBAND, SPINUP, i, XBAND, SPINUP)*
gl(i, YBAND, SPINUP, i, YBAND, SPINUP) + 2.0*
gl(i, YBAND, SPINDOWN, i, YBAND, SPINDOWN)*
gl(i, YBAND, SPINUP, i, YBAND, SPINUP);
}
occDiffSq += (std::real(occDiffSqContrib)) / num(N);
}
timing.stop("sdw-measure");
}
template<CheckerboardMethod CB, int OPDIM>
void DetSDW<CB, OPDIM>::finishMeasurements() {
//to ease notation:
const auto L = pars.L;
const auto N = pars.N;
const auto m = pars.m;
const auto dtau = pars.dtau;
assert(timeslices_included_in_measurement.size() == m);
//normphi, meanPhi, sdw-susceptibility
meanPhi /= num(N * m);
normMeanPhi = arma::norm(meanPhi, 2);
// bosonic spin stiffness
if (OPDIM == 2) {
phiRhoS_Gc *= (0.5 * dtau);
phiRhoS_Gs *= dtau;
}
associatedEnergy /= (2.0 * N * m);
if (not (pars.turnoffFermions or pars.turnoffFermionMeasurements)) {
if (pars.dumpGreensFunction) {
// some sectors of the momentum space Green's function
greenXUPXUP_summed /= num(m);
greenYDOWNYDOWN_summed /= num(m);
// computeStructureFactor(kgreenXUP, greenXUPXUP_summed);
// computeStructureFactor(kgreenYDOWN, greenYDOWNYDOWN_summed);
if (OPDIM == 3) {
greenXDOWNXDOWN_summed /= num(m);
greenYUPYUP_summed /= num(m);
// computeStructureFactor(kgreenXDOWN, greenXDOWNXDOWN_summed);
// computeStructureFactor(kgreenYUP, greenYUPYUP_summed);
} else {
// the following equalities are up to complex conjugation,
// but we only consider real parts anyway
// kgreenXDOWN = kgreenXUP;
// kgreenYUP = kgreenYDOWN;
}
greenXUPYDOWN_summed /= num(m);
greenYDOWNXUP_summed /= num(m);
// HACK - save current real-space Green's function
debugSaveMatrixCpx(greenXUPXUP_summed, "green_eqtime_realspace_XUPXUP_" + numToString(performedSweeps+1));
debugSaveMatrixCpx(greenXUPYDOWN_summed, "green_eqtime_realspace_XUPYDOWN_" + numToString(performedSweeps+1));
debugSaveMatrixCpx(greenYDOWNXUP_summed, "green_eqtime_realspace_YDOWNXUP_" + numToString(performedSweeps+1));
debugSaveMatrixCpx(greenYDOWNYDOWN_summed, "green_eqtime_realspace_YDOWNYDOWN_" + numToString(performedSweeps+1));
}
// scalar functions of the Green's function
greenK0 /= num(m);
greenLocal /= num(m);
// //fermion occupation number -- real space
// occX /= num(m * N);
// occY /= num(m * N);
//fermion occupation number -- k-space
for (uint32_t ksite = 0; ksite < N; ++ksite) {
// add 2.0 and not 1.0 because spin is included
kOccX[ksite] = 2.0 - kOccX[ksite] / num(m * N);
kOccY[ksite] = 2.0 - kOccY[ksite] / num(m * N);
}
//equal-time pairing-correlations
//-------------------------------
pairPlus /= m;
pairMinus /= m;
// sites around the maximum range L/2, L/2
static const uint32_t numSitesFar = 9;
uint32_t sitesfar[numSitesFar] = {
coordsToSite(L/2 - 1, L/2 - 1), coordsToSite(L/2, L/2 - 1), coordsToSite(L/2 + 1, L/2 - 1),
coordsToSite(L/2 - 1, L/2), coordsToSite(L/2, L/2), coordsToSite(L/2 + 1, L/2),
coordsToSite(L/2 - 1, L/2 + 1), coordsToSite(L/2, L/2 + 1), coordsToSite(L/2 + 1, L/2 + 1)
};
pairPlusMax = 0;
pairMinusMax = 0;
for (uint32_t i : sitesfar) {
pairPlusMax += pairPlus[i];
pairMinusMax += pairMinus[i];
}
pairPlusMax /= numSitesFar;
pairMinusMax /= numSitesFar;
// // Fermionic energy contribution
// // -----------------------------
// fermionEkinetic /= num(m*N);
// fermionEcouple /= num(m*N);
// // band occupation / charge correlations
// // -------------------------------------
// const Band BandValues[2] = {XBAND, YBAND};
// for (Band b1 : BandValues) {
// for (Band b2 : BandValues) {
// occCorr(b1,b2) /= num(m);