Commit dcd44908 authored by Alvarez, Gonzalo's avatar Alvarez, Gonzalo
Browse files

SU(3) model: started

parent 14be43f4
/*
Copyright (c) 2009, 2017-2019, UT-Battelle, LLC
All rights reserved
[DMRG++, Version 5.]
[by G.A., Oak Ridge National Laboratory]
UT Battelle Open Source Software License 11242008
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*/
/** \ingroup DMRG */
/*@{*/
/*! \file ModelHeisenberg.h
*
* An implementation of the Quantum Heisenberg Model to use with DmrgSolver
*
*/
#ifndef DMRG_MODEL_HEISENBERG_HEADER_H
#define DMRG_MODEL_HEISENBERG_HEADER_H
#include "Aklt.h"
#include <algorithm>
#include "ParametersModelHeisenberg.h"
#include "CrsMatrix.h"
#include "../../Engine/VerySparseMatrix.h"
#include "../../Engine/SpinSquaredHelper.h"
#include "../../Engine/SpinSquared.h"
#include "../../Engine/ProgramGlobals.h"
#include "../../Engine/Utils.h"
namespace Dmrg {
template<typename ModelBaseType>
class ModelHeisenberg : public ModelBaseType {
static const int NUMBER_OF_ORBITALS=1;
static const int DEGREES_OF_FREEDOM=2; // spin up and down
public:
typedef typename ModelBaseType::ModelHelperType ModelHelperType;
typedef typename ModelHelperType::BasisType BasisType;
typedef typename ModelBaseType::SuperGeometryType SuperGeometryType;
typedef typename ModelBaseType::LeftRightSuperType LeftRightSuperType;
typedef typename ModelBaseType::LinkType LinkType;
typedef typename ModelHelperType::OperatorsType OperatorsType;
typedef typename ModelHelperType::RealType RealType;
typedef typename ModelBaseType::VectorType VectorType;
typedef typename ModelBaseType::QnType QnType;
typedef typename ModelBaseType::VectorQnType VectorQnType;
typedef typename ModelBaseType::BlockType BlockType;
typedef typename ModelBaseType::SolverParamsType SolverParamsType;
typedef typename ModelHelperType::SparseMatrixType SparseMatrixType;
typedef typename SparseMatrixType::value_type ComplexOrRealType;
typedef unsigned int long WordType;
typedef typename ModelBaseType::InputValidatorType InputValidatorType;
typedef PsimagLite::Matrix<ComplexOrRealType> MatrixType;
typedef typename PsimagLite::Vector<SizeType>::Type VectorSizeType;
typedef typename ModelBaseType::VectorRealType VectorRealType;
typedef typename ModelBaseType::ModelTermType ModelTermType;
typedef typename PsimagLite::Vector<SizeType>::Type HilbertBasisType;
typedef typename OperatorsType::OperatorType OperatorType;
typedef typename OperatorType::PairType PairType;
typedef typename PsimagLite::Vector<OperatorType>::Type VectorOperatorType;
typedef typename ModelBaseType::MyBasis MyBasis;
typedef typename ModelBaseType::BasisWithOperatorsType MyBasisWithOperators;
typedef typename ModelBaseType::OpsLabelType OpsLabelType;
typedef typename ModelBaseType::OpForLinkType OpForLinkType;
typedef Aklt<ModelBaseType> AkltType;
ModelHeisenberg(const SolverParamsType& solverParams,
InputValidatorType& io,
const SuperGeometryType& geometry,
PsimagLite::String additional)
: ModelBaseType(solverParams,
geometry,
io),
modelParameters_(io),
superGeometry_(geometry),
additional_(additional),
spinSquared_(spinSquaredHelper_,NUMBER_OF_ORBITALS,DEGREES_OF_FREEDOM),
aklt_(*this, additional)
{
SizeType n = superGeometry_.numberOfSites();
SizeType m = modelParameters_.magneticFieldV.size();
SizeType md = modelParameters_.anisotropyD.size();
SizeType me = modelParameters_.anisotropyE.size();
if (m > 0 && m != n) {
PsimagLite::String msg("ModelHeisenberg: If provided, ");
msg += " MagneticField must be a vector of " + ttos(n) + " entries.\n";
err(msg);
}
if (md > 0 && md != n) {
PsimagLite::String msg("ModelHeisenberg: If provided, ");
msg += " AnisotropyD must be a vector of " + ttos(n) + " entries.\n";
throw PsimagLite::RuntimeError(msg);
}
if (me > 0 && me != n) {
PsimagLite::String msg("ModelHeisenberg: If provided, ");
msg += " AnisotropyE must be a vector of " + ttos(n) + " entries.\n";
throw PsimagLite::RuntimeError(msg);
}
if (BasisType::useSu2Symmetry() && modelParameters_.twiceTheSpin != 1) {
PsimagLite::String msg("ModelHeisenberg: SU(2) symmetry, ");
msg += " for spin different than 1/2 is not implemented yet.\n";
throw PsimagLite::RuntimeError(msg);
}
}
void write(PsimagLite::String label1, PsimagLite::IoNg::Out::Serializer& io) const
{
if (!io.doesGroupExist(label1))
io.createGroup(label1);
PsimagLite::String label = label1 + "/" + this->params().model;
io.createGroup(label);
modelParameters_.write(label, io);
spinSquaredHelper_.write(label, io);
spinSquared_.write(label, io);
}
/* PSIDOC Heisenberg::addDiagonalsInNaturalBasis
We describe only the addition of a Zeeman term to the Heisenberg model here; note
that this function is more complicated.
Please look carefully at the following C++ lines:
PSIDOCCOPY $FirstFunctionBelow::MagneticField
*/
void addDiagonalsInNaturalBasis(SparseMatrixType &hmatrix,
const BlockType& block,
RealType) const
{
SizeType linSize = superGeometry_.numberOfSites();
SizeType n = block.size();
for (SizeType i = 0; i < n; ++i) {
// PSIDOCMARK_BEGIN MagneticField
SizeType site = block[i];
const OperatorType& sz = ModelBaseType::naturalOperator("sz", site, 0);
const OperatorType& splus = ModelBaseType::naturalOperator("splus", site, 0);
if (modelParameters_.magneticFieldV.size() == linSize) {
RealType tmp = modelParameters_.magneticFieldV[site];
const OperatorType& sminus = ModelBaseType::naturalOperator("sminus", site, 0);
if (modelParameters_.magneticFieldDirection == "z") {
hmatrix += tmp*sz.getCRS();
} else if (modelParameters_.magneticFieldDirection == "x") {
static const RealType zeroPointFive = 0.5;
hmatrix += zeroPointFive*tmp*splus.getCRS();
hmatrix += zeroPointFive*tmp*sminus.getCRS();
}
}
// PSIDOCMARK_END
// anisotropyD
if (modelParameters_.anisotropyD.size() == linSize) {
SparseMatrixType Szsquare;
RealType tmp = modelParameters_.anisotropyD[site];
multiply(Szsquare, sz.getCRS(), sz.getCRS());
hmatrix += tmp*Szsquare;
}
// anisotropyE
if (modelParameters_.anisotropyE.size() == linSize) {
SparseMatrixType splusSquared;
RealType tmp = 0.5*modelParameters_.anisotropyE[site];
multiply(splusSquared, splus.getCRS(), splus.getCRS());
hmatrix += tmp*splusSquared;
SparseMatrixType sminusSquared;
transposeConjugate(sminusSquared, splusSquared);
hmatrix += tmp*sminusSquared;
}
}
}
protected:
void fillLabeledOperators(VectorQnType& qns)
{
SizeType site = 0;
BlockType block(1, site);
SizeType total = utils::powUint(modelParameters_.twiceTheSpin + 1, block.size());
HilbertBasisType natBasis(total);
for (SizeType i = 0; i < total; ++i) natBasis[i] = i;
setSymmetryRelated(qns, natBasis, block.size());
for (SizeType i=0;i<block.size();i++) {
// Set the operators S^+_i in the natural basis
SparseMatrixType tmpMatrix = findSplusMatrices(i,natBasis);
typename OperatorType::Su2RelatedType su2related;
su2related.source.push_back(i*DEGREES_OF_FREEDOM);
su2related.source.push_back(i*DEGREES_OF_FREEDOM+NUMBER_OF_ORBITALS);
su2related.source.push_back(i*DEGREES_OF_FREEDOM);
su2related.transpose.push_back(-1);
su2related.transpose.push_back(-1);
su2related.transpose.push_back(1);
su2related.offset = NUMBER_OF_ORBITALS;
OperatorType myOp(tmpMatrix,
ProgramGlobals::FermionOrBosonEnum::BOSON,
PairType(2, 2),
-1,
su2related);
this->createOpsLabel("splus").push(myOp);
this->makeTrackable("splus");
myOp.dagger();
this->createOpsLabel("sminus").push(myOp);
// Set the operators S^z_i in the natural basis
tmpMatrix = findSzMatrices(i,natBasis);
typename OperatorType::Su2RelatedType su2related2;
OperatorType myOp2(tmpMatrix,
ProgramGlobals::FermionOrBosonEnum::BOSON,
PairType(2, 1),
1.0/sqrt(2.0),
su2related2);
this->createOpsLabel("sz").push(myOp2);
this->makeTrackable("sz");
// Set the operators S^x_i in the natural basis
tmpMatrix = findSxMatrices(i,natBasis);
typename OperatorType::Su2RelatedType su2related3;
OperatorType myOp3(tmpMatrix,
ProgramGlobals::FermionOrBosonEnum::BOSON,
PairType(2, 1),
1.0/sqrt(2.0),
su2related3);
this->createOpsLabel("sx").push(myOp3);
if (additional_ == "Anisotropic")
this->makeTrackable("sx");
aklt_.fillLabeledOperators(i, myOp.getCRS(), myOp2.getCRS());
tmpMatrix = findMaximal(i, natBasis);
OperatorType myOp4(tmpMatrix,
ProgramGlobals::FermionOrBosonEnum::BOSON,
PairType(2, 1),
1.0/sqrt(2.0),
su2related3);
this->createOpsLabel("maximal").push(myOp4);
}
}
void fillModelLinks()
{
bool isSu2 = BasisType::useSu2Symmetry();
ModelTermType& spsm = ModelBaseType::createTerm("SplusSminus");
OpForLinkType splus("splus");
auto valueModiferTerm0 = [isSu2](ComplexOrRealType& value)
{ value *= (isSu2) ? -0.5 : 0.5;};
typename ModelTermType::Su2Properties su2properties(2, -1, 2);
spsm.push(splus, 'N', splus, 'C', valueModiferTerm0, su2properties);
ModelTermType& szsz = ModelBaseType::createTerm("szsz");
if (!isSu2) {
OpForLinkType sz("sz");
szsz.push(sz, 'N', sz, 'N', typename ModelTermType::Su2Properties(2, 0.5));
} else {
auto valueModifierTermOther = [isSu2](ComplexOrRealType& value)
{ if (isSu2) value = -value;};
typename ModelTermType::Su2Properties su2properties(2, -1, 2);
spsm.push(splus, 'N', splus, 'C', valueModifierTermOther, su2properties);
}
if (additional_ == "Anisotropic") {
ModelTermType& sxsx = ModelBaseType::createTerm("sxsx");
OpForLinkType sx("sx");
sxsx.push(sx, 'N', sx, 'N', typename ModelTermType::Su2Properties(2, 1, 0));
}
aklt_.fillModelLinks();
}
private:
//! Find S^+_site in the natural basis natBasis
SparseMatrixType findSplusMatrices(SizeType site,
const HilbertBasisType& natBasis) const
{
SizeType total = natBasis.size();
MatrixType cm(total,total);
RealType j = 0.5*modelParameters_.twiceTheSpin;
SizeType bitsForOneSite = utils::bitSizeOfInteger(modelParameters_.twiceTheSpin);
SizeType bits = 1 + ProgramGlobals::logBase2(modelParameters_.twiceTheSpin);
SizeType mask = 1;
mask <<= bits; // mask = 2^bits
assert(mask > 0);
mask--;
mask <<= (site*bitsForOneSite);
for (SizeType ii=0;ii<total;ii++) {
SizeType ket = natBasis[ii];
SizeType ketsite = ket & mask;
ketsite >>= (site*bitsForOneSite);
assert(ketsite == ket);
SizeType brasite = ketsite + 1;
if (brasite >= modelParameters_.twiceTheSpin+1) continue;
SizeType bra = ket & (~mask);
assert(bra == 0);
brasite <<= (site*bitsForOneSite);
bra |= brasite;
assert(bra == brasite);
RealType m = ketsite - j;
RealType x = j*(j+1)-m*(m+1);
assert(x>=0);
cm(ket,bra) = sqrt(x);
}
SparseMatrixType operatorMatrix(cm);
return operatorMatrix;
}
//! Find S^z_i in the natural basis natBasis
SparseMatrixType findSzMatrices(SizeType site,
const HilbertBasisType& natBasis) const
{
SizeType total = natBasis.size();
MatrixType cm(total,total);
RealType j = 0.5*modelParameters_.twiceTheSpin;
SizeType bitsForOneSite = utils::bitSizeOfInteger(modelParameters_.twiceTheSpin);
SizeType bits = ProgramGlobals::logBase2(modelParameters_.twiceTheSpin) + 1;
SizeType mask = 1;
mask <<= bits; // mask = 2^bits
assert(mask > 0);
mask--;
mask <<= (site*bitsForOneSite);
for (SizeType ii=0;ii<total;ii++) {
SizeType ket = natBasis[ii];
SizeType ketsite = ket & mask;
ketsite >>= (site*bitsForOneSite);
assert(ketsite == ket);
RealType m = ketsite - j;
cm(ket,ket) = m;
}
SparseMatrixType operatorMatrix(cm);
return operatorMatrix;
}
//! Find Maximal_i in the natural basis natBasis
SparseMatrixType findMaximal(SizeType site,
const HilbertBasisType& natBasis) const
{
SizeType total = natBasis.size();
MatrixType cm(total,total);
SizeType bitsForOneSite = utils::bitSizeOfInteger(modelParameters_.twiceTheSpin);
SizeType bits = ProgramGlobals::logBase2(modelParameters_.twiceTheSpin) + 1;
SizeType mask = 1;
mask <<= bits; // mask = 2^bits
assert(mask > 0);
mask--;
mask <<= (site*bitsForOneSite);
for (SizeType ii=0;ii<total;ii++) {
SizeType ket = natBasis[ii];
SizeType ketsite = ket & mask;
ketsite >>= (site*bitsForOneSite);
assert(ketsite == ket);
if (ketsite != modelParameters_.twiceTheSpin)
continue;
cm(ket, ket) = 1;
}
SparseMatrixType operatorMatrix(cm);
return operatorMatrix;
}
SparseMatrixType findSxMatrices(SizeType site,
const HilbertBasisType& natBasis) const
{
SparseMatrixType Splus_temp=findSplusMatrices(site,natBasis);
SparseMatrixType Sminus_temp,Sx;
transposeConjugate(Sminus_temp,Splus_temp);
RealType tmp=0.5;
Sx = tmp*Splus_temp;
Sx += tmp*Sminus_temp;
return Sx;
}
void setSymmetryRelated(VectorQnType& qns,
const HilbertBasisType& basis,
int n) const
{
// find j,m and flavors (do it by hand since we assume n==1)
// note: we use 2j instead of j
// note: we use m+j instead of m
// This assures us that both j and m are SizeType
typedef std::pair<SizeType,SizeType> PairType;
bool isCanonical = (ModelBaseType::targetQuantum().sizeOfOther() == 1);
if (isCanonical && additional_ == "Anisotropic")
err(PsimagLite::String(__FILE__) +
": Anisotropic sub-model CANNOT be canonical. Please " +
"delete the TargetSzPlusConst= from the input file\n");
if (isCanonical && modelParameters_.magneticFieldDirection == "x")
err(PsimagLite::String(__FILE__) +
": magneticFieldDirection == x CANNOT be canonical. Please " +
"delete the TargetSzPlusConst= from the input file\n");
VectorSizeType other;
if (isCanonical) other.resize(1, 0);
QnType::ifPresentOther0IsElectrons = false;
qns.resize(basis.size(), QnType::zero());
for (SizeType i = 0; i < basis.size(); ++i) {
PairType jmpair(modelParameters_.twiceTheSpin, basis[i]);
if (isCanonical)
other[0] = getSzPlusConst(basis[i], n);
SizeType flavor = 1;
qns[i] = QnType(false, other, jmpair, flavor);
}
}
SizeType getSzPlusConst(SizeType ket, SizeType n) const
{
if (n == 1) return ket;
SizeType bitsForOneSite = utils::bitSizeOfInteger(modelParameters_.twiceTheSpin);
SizeType sum = 0;
for (SizeType site = 0; site < n; ++site) {
SizeType mask = modelParameters_.twiceTheSpin;
mask <<= (site*bitsForOneSite);
SizeType ketsite = ket & mask;
ketsite >>= (site*bitsForOneSite);
sum += ketsite;
}
return sum;
}
ParametersModelHeisenberg<RealType, QnType> modelParameters_;
const SuperGeometryType& superGeometry_;
SpinSquaredHelper<RealType,WordType> spinSquaredHelper_;
PsimagLite::String additional_;
SpinSquared<SpinSquaredHelper<RealType,WordType> > spinSquared_;
AkltType aklt_;
}; // class ModelHeisenberg
} // namespace Dmrg
/*@}*/
#endif //DMRG_MODEL_HEISENBERG_HEADER_H
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