/**********************************************************
This software is part of J.-S. Caux's ABACUS library.
Copyright (c) J.-S. Caux.
-----------------------------------------------------------
File: ABACUS_ODSLF.h
Purpose: Declares lattice spinless fermion classes and functions.
***********************************************************/
#ifndef ABACUS_ODSLF_H
#define ABACUS_ODSLF_H
#include "ABACUS.h"
namespace ABACUS {
//****************************************************************************
// Objects in class ODSLF_Base are a checked vector containing the number of rapidities of allowable types for a given state
class ODSLF_Base {
public:
int Mdown; // total number of down spins
Vect<int> Nrap; // Nrap[i] contains the number of rapidities of type i, i = 0, Nstrings - 1.
int Nraptot; // total number of strings in this state
Vect<DP> Ix2_infty; // Ix2_infty[i] contains the max of BAE function for the (half-)integer I[i], i = 0, Nstrings - 1.
Vect<int> Ix2_max; // Ix2_max[i] contains the integer part of 2*I_infty, with correct parity for base.
long long int id; // identification number
public:
ODSLF_Base ();
ODSLF_Base (const ODSLF_Base& RefBase); // copy constructor
ODSLF_Base (const Heis_Chain& RefChain, int M); // constructs configuration with all Mdown in one-string of +1 parity
ODSLF_Base (const Heis_Chain& RefChain, const Vect<int>& Nrapidities); // sets to Nrapidities vector, and checks consistency
ODSLF_Base (const Heis_Chain& RefChain, long long int id_ref);
inline int& operator[] (const int i);
inline const int& operator[] (const int i) const;
ODSLF_Base& operator= (const ODSLF_Base& RefBase);
bool operator== (const ODSLF_Base& RefBase);
bool operator!= (const ODSLF_Base& RefBase);
void Compute_Ix2_limits(const Heis_Chain& RefChain); // computes the Ix2_infty and Ix2_max
void Scan_for_Possible_Types (Vect<long long int>& possible_type_id, int& nfound, int base_level, Vect<int>& Nexcitations);
Vect<long long int> Possible_Types (); // returns a vector of possible types
};
inline int& ODSLF_Base::operator[] (const int i)
{
return Nrap[i];
}
inline const int& ODSLF_Base::operator[] (const int i) const
{
return Nrap[i];
}
//****************************************************************************
// Objects in class ODSLF_Ix2_Config carry all the I's of a given state
class ODSLF_Ix2_Config {
public:
int Nstrings;
Vect<int> Nrap;
int Nraptot;
int** Ix2;
public:
ODSLF_Ix2_Config ();
ODSLF_Ix2_Config (const Heis_Chain& RefChain, int M); // constructor, puts I's to ground state
ODSLF_Ix2_Config (const Heis_Chain& RefChain, const ODSLF_Base& base); // constructor, putting I's to lowest-energy config
// consistent with Heis_Base configuration for chain RefChain
ODSLF_Ix2_Config& operator= (const ODSLF_Ix2_Config& RefConfig);
inline int* operator[] (const int i);
inline const int* operator[] (const int i) const;
~ODSLF_Ix2_Config();
};
inline int* ODSLF_Ix2_Config::operator[] (const int i)
{
return Ix2[i];
}
inline const int* ODSLF_Ix2_Config::operator[] (const int i) const
{
return Ix2[i];
}
std::ostream& operator<< (std::ostream& s, const ODSLF_Ix2_Config& RefConfig);
//****************************************************************************
// Objects in class ODSLF_Lambda carry all rapidities of a state
class ODSLF_Lambda {
private:
int Nstrings;
Vect<int> Nrap;
int Nraptot;
DP** lambda;
public:
ODSLF_Lambda ();
ODSLF_Lambda (const Heis_Chain& RefChain, int M); // constructor, puts all lambda's to zero
ODSLF_Lambda (const Heis_Chain& RefChain, const ODSLF_Base& base); // constructor, putting I's to lowest-energy config
// consistent with Heis_Base configuration for chain RefChain
ODSLF_Lambda& operator= (const ODSLF_Lambda& RefConfig);
inline DP* operator[] (const int i);
inline const DP* operator[] (const int i) const;
~ODSLF_Lambda();
};
inline DP* ODSLF_Lambda::operator[] (const int i)
{
return lambda[i];
}
inline const DP* ODSLF_Lambda::operator[] (const int i) const
{
return lambda[i];
}
//****************************************************************************
// Objects in class ODSLF_Ix2_Offsets carry Young tableau representations of the Ix2 configurations
class ODSLF_Ix2_Offsets {
public:
ODSLF_Base base;
Vect<Young_Tableau> Tableau; // vector of pointers to tableaux at each level
long long int type_id;
long long int id; // id number of offset
long long int maxid; // max id number allowable
public:
ODSLF_Ix2_Offsets ();
ODSLF_Ix2_Offsets (const ODSLF_Ix2_Offsets& RefOffset); // copy constructor
ODSLF_Ix2_Offsets (const ODSLF_Base& RefBase, long long int req_type_id);
ODSLF_Ix2_Offsets (const ODSLF_Base& RefBase, Vect<int> nparticles); // sets all tableaux to empty ones, with nparticles[] at each level
ODSLF_Ix2_Offsets& operator= (const ODSLF_Ix2_Offsets& RefOffset);
bool operator<= (const ODSLF_Ix2_Offsets& RefOffsets);
bool operator>= (const ODSLF_Ix2_Offsets& RefOffsets);
public:
void Set_to_id (long long int idnr);
void Compute_id ();
void Compute_type_id ();
public:
bool Add_Boxes_From_Lowest (int Nboxes, bool odd_sectors); // adds Nboxes in minimal energy config, all boxes in either even or odd sectors
};
inline long long int ODSLF_Ix2_Offsets_type_id (Vect<int>& nparticles)
{
long long int type_id_here = 0ULL;
for (int i = 0; i < nparticles.size(); ++i)
type_id_here += nparticles[i] * pow_ulli(10ULL, i);
return(type_id_here);
}
//****************************************************************************
// Objects in class ODSLF_Ix2_Offsets_List carry a vector of used Ix2_Offsets
class ODSLF_Ix2_Offsets_List {
public:
int ndef;
Vect<ODSLF_Ix2_Offsets> Offsets;
public:
ODSLF_Ix2_Offsets_List ();
ODSLF_Ix2_Offsets& Return_Offsets (ODSLF_Base& RefBase, Vect<int> nparticles); // returns the Ix2_Offsets corresponding to nparticles[]/base
ODSLF_Ix2_Offsets& Return_Offsets (ODSLF_Base& RefBase, long long int req_type_id);
};
//****************************************************************************
// Objects in class ODSLF_Bethe_State carry all information about an eigenstate
// Derived classes include XXZ_Bethe_State, XXX_Bethe_State, XXZ_gpd_Bethe_State
// These contain subclass-specific functions and data.
class ODSLF_Bethe_State {
public:
Heis_Chain chain;
ODSLF_Base base;
ODSLF_Ix2_Offsets offsets;
ODSLF_Ix2_Config Ix2;
ODSLF_Lambda lambda;
ODSLF_Lambda BE; // Bethe equation for relevant rapidity, in the form BE = theta - (1/N)\sum ... - \pi I/N = 0
DP diffsq; // sum of squares of rapidity differences in last iteration
int conv; // convergence status
int iter; // number of iterations necessary for convergence
int iter_Newton; // number of iterations necessary for convergence (Newton method)
DP E; // total energy
int iK; // K = 2.0*PI * iK/Nsites
DP K; // total momentum
DP lnnorm; // ln of norm of reduced Gaudin matrix
long long int base_id;
long long int type_id;
long long int id;
long long int maxid;
int nparticles;
public:
ODSLF_Bethe_State ();
ODSLF_Bethe_State (const ODSLF_Bethe_State& RefState); // copy constructor
ODSLF_Bethe_State (const ODSLF_Bethe_State& RefState, long long int type_id_ref); // new state with requested type_id
ODSLF_Bethe_State (const Heis_Chain& RefChain, int M); // constructor to ground-state configuration
ODSLF_Bethe_State (const Heis_Chain& RefChain, const ODSLF_Base& base); // constructor to lowest-energy config with base
ODSLF_Bethe_State (const Heis_Chain& RefChain, long long int base_id_ref, long long int type_id_ref);
virtual ~ODSLF_Bethe_State () {};
public:
int Charge () { return(base.Mdown); };
void Set_Ix2_Offsets (const ODSLF_Ix2_Offsets& RefOffset); // sets the Ix2 to given offsets
void Set_to_id (long long int id_ref);
void Set_to_id (long long int id_ref, ODSLF_Bethe_State& RefState);
int Nparticles (); // counts the number of particles in state once Ix2 offsets set (so type_id is correctly set)
bool Check_Symmetry (); // checks whether the I's are symmetrically distributed
void Compute_diffsq (); // \sum BE[j][alpha]^2
void Iterate_BAE (); // Finds new set of lambda[j][alpha] from previous one by simple iteration
void Iterate_BAE_Newton (); // Finds new set of lambda[j][alpha] from previous one by a Newton step
void Find_Rapidities (bool reset_rapidities); // Finds the rapidities
void Find_Rapidities_Twisted (bool reset_rapidities, DP twist); // Finds the rapidities with twist added to RHS of logBE
void BAE_smackdown (DP max_allowed);
void Solve_BAE_smackdown (DP max_allowed, int maxruns);
void Solve_BAE (int j, int alpha, DP req_prec, int itermax);
void Solve_BAE_interp (DP interp_prec, int max_iter_interp);
void Solve_BAE_straight_iter (DP interp_prec, int max_iter_interp);
void Solve_BAE_Newton (DP Newton_prec, int max_iter_Newton);
void Compute_lnnorm ();
void Compute_Momentum ();
void Compute_All (bool reset_rapidities); // solves BAE, computes E, K and lnnorm
bool Boost_Momentum (int iKboost);
// Virtual functions, all defined in the derived classes
public:
virtual void Set_Free_lambdas() { ABACUSerror("ODSLF_Bethe_State::..."); } // sets the rapidities to solutions of BAEs without scattering terms
virtual bool Check_Admissibility(char option) { ABACUSerror("ODSLF_Bethe_State::..."); return(false); }
// verifies that we don't have a symmetrical Ix2 config with a Ix2 == 0 for a string of even length >= 2.
virtual void Compute_BE (int j, int alpha) { ABACUSerror("ODSLF_Bethe_State::..."); }
virtual void Compute_BE () { ABACUSerror("ODSLF_Bethe_State::..."); }
virtual DP Iterate_BAE(int i, int alpha) { ABACUSerror("ODSLF_Bethe_State::..."); return(0.0);}
virtual bool Check_Rapidities() { ABACUSerror("ODSLF_Bethe_State::..."); return(false); }
virtual void Compute_Energy () { ABACUSerror("ODSLF_Bethe_State::..."); }
virtual void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red) { ABACUSerror("ODSLF_Bethe_State::..."); }
};
inline bool Force_Descent (char whichDSF, ODSLF_Bethe_State& ScanState, ODSLF_Bethe_State& RefState, int desc_type_required, int iKmod, DP Chem_Pot)
{
ABACUSerror("Need to implement Force_Descent properly for ODSLF.");
bool force_descent = false;
// Force descent if quantum nr distribution is symmetric:
if (RefState.Check_Symmetry()) force_descent = true;
return(force_descent);
}
std::ostream& operator<< (std::ostream& s, const ODSLF_Bethe_State& state);
//****************************************************************************
// Objects in class XXZ_Bethe_State carry all extra information pertaining to XXZ gapless
class ODSLF_XXZ_Bethe_State : public ODSLF_Bethe_State {
public:
ODSLF_Lambda sinhlambda;
ODSLF_Lambda coshlambda;
ODSLF_Lambda tanhlambda;
public:
ODSLF_XXZ_Bethe_State ();
ODSLF_XXZ_Bethe_State (const ODSLF_XXZ_Bethe_State& RefState); // copy constructor
ODSLF_XXZ_Bethe_State (const Heis_Chain& RefChain, int M); // constructor to ground-state configuration
ODSLF_XXZ_Bethe_State (const Heis_Chain& RefChain, const ODSLF_Base& base); // constructor to lowest-energy config with base
ODSLF_XXZ_Bethe_State (const Heis_Chain& RefChain, long long int base_id_ref, long long int type_id_ref); // constructor to lowest-energy config with bas
public:
ODSLF_XXZ_Bethe_State& operator= (const ODSLF_XXZ_Bethe_State& RefState);
public:
void Set_Free_lambdas(); // sets the rapidities to solutions of BAEs without scattering terms
void Compute_sinhlambda();
void Compute_coshlambda();
void Compute_tanhlambda();
bool Check_Admissibility(char option); // verifies that we don't have a symmetrical Ix2 config with a Ix2 == 0 for a string of even length >= 2.
void Compute_BE (int j, int alpha);
void Compute_BE ();
DP Iterate_BAE(int i, int j);
bool Check_Rapidities(); // checks that all rapidities are not nan
void Compute_Energy ();
void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red);
// XXZ specific functions:
public:
};
//****************************************************************************
/*
// Objects in class ODSLF_XXX_Bethe_State carry all extra information pertaining to XXX antiferromagnet
class ODSLF_XXX_Bethe_State : public ODSLF_Bethe_State {
public:
ODSLF_XXX_Bethe_State ();
ODSLF_XXX_Bethe_State (const ODSLF_XXX_Bethe_State& RefState); // copy constructor
ODSLF_XXX_Bethe_State (const Heis_Chain& RefChain, int M); // constructor to ground-state configuration
ODSLF_XXX_Bethe_State (const Heis_Chain& RefChain, const ODSLF__Base& base); // constructor to lowest-energy config with base
ODSLF_XXX_Bethe_State (const Heis_Chain& RefChain, long long int base_id_ref, long long int type_id_ref); // constructor to lowest-energy config with base
public:
ODSLF_XXX_Bethe_State& operator= (const ODSLF_XXX_Bethe_State& RefState);
public:
void Set_Free_lambdas(); // sets the rapidities to solutions of BAEs without scattering terms
bool Check_Admissibility(char option); // verifies that we don't have a symmetrical Ix2 config with a Ix2 == 0 for a string of even length >= 2.
void Compute_BE (int j, int alpha);
void Compute_BE ();
DP Iterate_BAE(int i, int j);
bool Check_Rapidities(); // checks that all rapidities are not nan
void Compute_Energy ();
//void Compute_Momentum ();
void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red);
// XXX specific functions
public:
bool Check_Finite_rap ();
};
*/
//****************************************************************************
/*
// Objects in class ODSLF_XXZ_gpd_Bethe_State carry all extra information pertaining to XXZ gapped antiferromagnets
class ODSLF_XXZ_gpd_Bethe_State : public ODSLF__Bethe_State {
public:
Lambda sinlambda;
Lambda coslambda;
Lambda tanlambda;
public:
ODSLF_XXZ_gpd_Bethe_State ();
ODSLF_XXZ_gpd_Bethe_State (const ODSLF_XXZ_gpd_Bethe_State& RefState); // copy constructor
ODSLF_XXZ_gpd_Bethe_State (const Heis_Chain& RefChain, int M); // constructor to ground-state configuration
ODSLF_XXZ_gpd_Bethe_State (const Heis_Chain& RefChain, const ODSLF_Base& base); // constructor to lowest-energy config with base
ODSLF_XXZ_gpd_Bethe_State (const Heis_Chain& RefChain, long long int base_id_ref, long long int type_id_ref); // constructor to lowest-energy config with base
public:
ODSLF_XXZ_gpd_Bethe_State& operator= (const ODSLF_XXZ_gpd_Bethe_State& RefState);
public:
void Set_Free_lambdas(); // sets the rapidities to solutions of BAEs without scattering terms
void Compute_sinlambda();
void Compute_coslambda();
void Compute_tanlambda();
int Weight(); // weight function for contributions cutoff
bool Check_Admissibility(char option); // verifies that we don't have a symmetrical Ix2 config with a Ix2 == 0 for a string of even length >= 2.
void Compute_BE (int j, int alpha);
void Compute_BE ();
DP Iterate_BAE(int i, int j);
void Iterate_BAE_Newton();
bool Check_Rapidities(); // checks that all rapidities are not nan and are in interval ]-PI/2, PI/2]
void Compute_Energy ();
//void Compute_Momentum ();
void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red);
// XXZ_gpd specific functions
public:
};
*/
//***********************************************
// Function declarations
/*
// in M_vs_H.cc
DP Ezero (DP Delta, int N, int M);
DP H_vs_M (DP Delta, int N, int M);
DP HZmin (DP Delta, int N, int M, Vect_DP& Ezero_ref);
int M_vs_H (DP Delta, int N, DP HZ);
DP X_avg (char xyorz, DP Delta, int N, int M);
*/
DP Chemical_Potential (const ODSLF_Bethe_State& RefState);
DP Sumrule_Factor (char whichDSF, ODSLF_Bethe_State& RefState, DP Chem_Pot, int iKmin, int iKmax);
void Evaluate_F_Sumrule (std::string prefix, char whichDSF, const ODSLF_Bethe_State& RefState, DP Chem_Pot, int iKmin, int iKmax);
std::complex<DP> ln_Sz_ME (ODSLF_XXZ_Bethe_State& A, ODSLF_XXZ_Bethe_State& B);
std::complex<DP> ln_Smin_ME (ODSLF_XXZ_Bethe_State& A, ODSLF_XXZ_Bethe_State& B);
DP Compute_Matrix_Element_Contrib (char whichDSF, int iKmin, int iKmax, ODSLF_XXZ_Bethe_State& LeftState,
ODSLF_XXZ_Bethe_State& RefState, DP Chem_Pot, std::stringstream& DAT_outfile);
} // namespace ABACUS
#endif