ABACUS/include/ABACUS_Heis.h

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

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

Copyright (c) J.-S. Caux.

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

File:  ABACUS_Heis.h

Purpose:  Declares Heisenberg chain classes and functions.

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

#ifndef ABACUS_HEIS_H
#define ABACUS_HEIS_H

#include "ABACUS.h"

namespace ABACUS {

  // First, some global constants...

  const long long int ID_UPPER_LIMIT = 10000000LL;  // max size we can define without seg fault
  const int INTERVALS_SIZE = 100000;                // size of Scan_Intervals arrays
  const int NBASESMAX = 1000; // max number of bases kept

  const DP ITER_REQ_PREC = 100.0 * MACHINE_EPS_SQ;

  // Cutoffs on particle numbers
  const int MAXSTRINGS = 20;      // maximal number of particle types we allow in bases

  const int NEXC_MAX_HEIS = 16; // max nr of excitations (string binding/unbinding, particle-hole) considered


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

  class Heis_Chain {

  public:
    DP J;
    DP Delta;
    DP anis;  // acos(Delta) if Delta < 1.0, 0 if Delta == 1.0, acosh(Delta) if Delta > 1.0
    DP hz;
    int Nsites;
    int Nstrings;  // how many possible strings.  The following two arrays have Nstrings nonzero elements.
    int* Str_L; // vector (length M) containing the allowed string lengths.  Elements that are 0 have no meaning.
    int* par;    // vector (length M) containing the parities of the strings.  Elements that are 0 have no meaning.
    // Parities are all +1 except for gapless XXZ subcases
    DP* si_n_anis_over_2;  // for optimization: sin for XXZ, sinh for XXZ_gpd
    DP* co_n_anis_over_2;  // for optimization
    DP* ta_n_anis_over_2;  // for optimization
    DP prec;  // precision required for computations, always put to ITER_REQ_PREC

  public:
    Heis_Chain ();
    Heis_Chain (DP JJ, DP DD, DP hh, int NN);  // contructor:  simply initializes
    Heis_Chain (const Heis_Chain& RefChain);            // copy constructor;
    Heis_Chain& operator= (const Heis_Chain& RefChain);
    bool operator== (const Heis_Chain& RefChain);
    bool operator!= (const Heis_Chain& RefChain);
    ~Heis_Chain();  // destructor

  };


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

  // Objects in class Heis_Base are a checked vector containing the number of rapidities
  // of allowable types for a given state

  class Heis_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_min;
    Vect<int> Ix2_max;    // Ix2_max[i] contains the integer part of 2*I_infty, with correct parity for base.
    double dimH;          // dimension of sub Hilbert space associated to this base; use double to avoid max int problems.
    std::string baselabel;      // base label

  public:
    Heis_Base ();
    Heis_Base (const Heis_Base& RefBase);  // copy constructor
    Heis_Base (const Heis_Chain& RefChain, int M);  // constructs configuration with all Mdown in one-string of +1 parity
    Heis_Base (const Heis_Chain& RefChain, const Vect<int>& Nrapidities);  // sets to Nrapidities vector, and checks consistency
    Heis_Base (const Heis_Chain& RefChain, std::string baselabel_ref);
    inline int& operator[] (const int i);
    inline const int& operator[] (const int i) const;
    Heis_Base& operator= (const Heis_Base& RefBase);
    bool operator== (const Heis_Base& RefBase);
    bool operator!= (const Heis_Base& RefBase);

    void Compute_Ix2_limits(const Heis_Chain& RefChain);  // computes the Ix2_infty and Ix2_max

  };

  inline int& Heis_Base::operator[] (const int i)
  {
    return Nrap[i];
  }

  inline const int& Heis_Base::operator[] (const int i) const
  {
    return Nrap[i];
  }


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

  // Objects in class Lambda carry all rapidities of a state

  class Lambda {

  private:
    int Nstrings;
    Vect<int> Nrap;
    int Nraptot;
    DP** lambda;

  public:
    Lambda ();
    Lambda (const Heis_Chain& RefChain, int M);   // constructor, puts all lambda's to zero
    Lambda (const Heis_Chain& RefChain, const Heis_Base& base);   // constructor, putting I's to lowest-energy config
    // consistent with Heis_Base configuration for chain RefChain
    Lambda& operator= (const Lambda& RefConfig);
    inline DP* operator[] (const int i);
    inline const DP* operator[] (const int i) const;
    ~Lambda();

  };

  inline DP* Lambda::operator[] (const int i)
  {
    return lambda[i];
  }

  inline const DP* Lambda::operator[] (const int i) const
  {
    return lambda[i];
  }


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

  // Objects in class Heis_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 Heis_Bethe_State {

  public:
    Heis_Chain chain;
    Heis_Base base;
    Vect<Vect<int> > Ix2;
    Lambda lambda;
    Lambda deviation;      // string deviations
    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
    DP dev;                // sum of absolute values of string deviations
    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
    std::string label;

  public:
    Heis_Bethe_State ();
    Heis_Bethe_State (const Heis_Bethe_State& RefState);  // copy constructor
    Heis_Bethe_State (const Heis_Chain& RefChain, int M);  // constructor to ground-state configuration
    Heis_Bethe_State (const Heis_Chain& RefChain, const Heis_Base& base);  // constructor to lowest-energy config with base
    virtual ~Heis_Bethe_State () {};

  public:
    int Charge () { return(base.Mdown); };
    void Set_to_Label (std::string label_ref, const Vect<Vect<int> >& OriginIx2);
    void Set_Label_from_Ix2 (const Vect<Vect<int> >& OriginIx2);
    bool Check_Symmetry ();  // checks whether the I's are symmetrically distributed
    void Compute_diffsq ();  // \sum BE[j][alpha]^2
    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 Solve_BAE_bisect (int j, int alpha, DP req_prec, int itermax);
    void Iterate_BAE (DP iter_factor);     // Finds new set of lambda[j][alpha] from previous one by simple iteration
    void Solve_BAE_straight_iter (DP straight_prec, int max_iter_interp, DP iter_factor);
    void Solve_BAE_extrap (DP extrap_prec, int max_iter_extrap, DP iter_factor);
    void Iterate_BAE_Newton ();     // Finds new set of lambda[j][alpha] from previous one by a Newton step
    void Solve_BAE_Newton (DP Newton_prec, int max_iter_Newton);
    void Solve_BAE_with_silk_gloves (DP silk_prec, int max_iter_silk, DP iter_factor);
    void Compute_lnnorm ();
    void Compute_Momentum ();
    void Compute_All (bool reset_rapidities);     // solves BAE, computes E, K and lnnorm

    inline bool Set_to_Inner_Skeleton (int iKneeded, const Vect<Vect<int> >& OriginStateIx2)
    {
      Ix2[0][0] = Ix2[0][1] - 2;
      Ix2[0][base.Nrap[0] - 1] = Ix2[0][base.Nrap[0] - 2] + 2;
      (*this).Compute_Momentum();
      if (base.Nrap[0] == 0) return(false);
      if (iKneeded >= iK) Ix2[0][base.Nrap[0]-1] += 2*(iKneeded - iK);
      else Ix2[0][0] += 2*(iKneeded - iK);
      if (Ix2[0][0] < base.Ix2_min[0] || Ix2[0][base.Nrap[0]-1] > base.Ix2_max[0]) return(false);
      (*this).Set_Label_from_Ix2 (OriginStateIx2);
      return(true);
    }
    void Set_to_Outer_Skeleton (const Vect<Vect<int> >& OriginStateIx2) {
      Ix2[0][0] = base.Ix2_min[0] - 4;
      Ix2[0][base.Nrap[0]-1] = base.Ix2_max[0] + 4;
      (*this).Set_Label_from_Ix2 (OriginStateIx2);
    };

    void Set_to_Closest_Matching_Ix2_fixed_Base (const Heis_Bethe_State& StateToMatch); // defined in Heis.cc


    // Virtual functions, all defined in the derived classes

  public:
    virtual void Set_Free_lambdas() { ABACUSerror("Heis_Bethe_State::..."); }  // sets the rapidities to solutions of BAEs without scattering terms
    virtual bool Check_Admissibility(char option) { ABACUSerror("Heis_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("Heis_Bethe_State::..."); }
    virtual void Compute_BE () { ABACUSerror("Heis_Bethe_State::..."); }
    virtual DP Iterate_BAE(int i, int alpha) { ABACUSerror("Heis_Bethe_State::..."); return(0.0);}
    virtual bool Check_Rapidities() { ABACUSerror("Heis_Bethe_State::..."); return(false); }
    virtual DP String_delta () { ABACUSerror("Heis_Bethe_State::..."); return(0.0); }
    virtual void Compute_Energy () { ABACUSerror("Heis_Bethe_State::..."); }
    virtual void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red) { ABACUSerror("Heis_Bethe_State::..."); }
  };

  inline bool Is_Inner_Skeleton (Heis_Bethe_State& State) {
    return (State.base.Nrap[0] >= 2 && (State.Ix2[0][0] == State.Ix2[0][1] - 2 || State.Ix2[0][State.base.Nrap[0]-1] == State.Ix2[0][State.base.Nrap[0]-2] + 2));
  };
  inline bool Is_Outer_Skeleton (Heis_Bethe_State& State) {
    return (State.Ix2[0][0] == State.base.Ix2_min[0] - 4 && State.Ix2[0][State.base.Nrap[0]-1] == State.base.Ix2_max[0] + 4);
  };

  inline bool Force_Descent (char whichDSF, Heis_Bethe_State& ScanState, Heis_Bethe_State& RefState, int desc_type_required, int iKmod, DP Chem_Pot)
  {
    bool force_descent = false;

    // Force descent for all DSFs if we're at K = 0 or PI and not conserving momentum upon descent:
    if (desc_type_required > 8 && (2*(ScanState.iK - RefState.iK) % iKmod == 0)) force_descent = true; // type_req > 8 means that we don't conserve momentum

    return(force_descent);
  }


  std::ostream& operator<< (std::ostream& s, const Heis_Bethe_State& state);


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

  // Objects in class XXZ_Bethe_State carry all extra information pertaining to XXZ gapless

  class XXZ_Bethe_State : public Heis_Bethe_State {

  public:
    Lambda sinhlambda;
    Lambda coshlambda;
    Lambda tanhlambda;

  public:
    XXZ_Bethe_State ();
    XXZ_Bethe_State (const XXZ_Bethe_State& RefState);  // copy constructor
    XXZ_Bethe_State (const Heis_Chain& RefChain, int M);  // constructor to ground-state configuration
    XXZ_Bethe_State (const Heis_Chain& RefChain, const Heis_Base& base);  // constructor to lowest-energy config with base

  public:
    XXZ_Bethe_State& operator= (const 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
    DP String_delta ();
    void Compute_Energy ();
    void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red);

    // XXZ specific functions:
  public:

  };

  XXZ_Bethe_State Add_Particle_at_Center (const XXZ_Bethe_State& RefState);
  XXZ_Bethe_State Remove_Particle_at_Center (const XXZ_Bethe_State& RefState);

  // Defined in XXZ_Bethe_State.cc
  inline DP fbar_XXZ (DP lambda, int par, DP tannzetaover2);
  DP Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* tannzetaover2);
  DP hbar_XXZ (DP lambda, int n, int par, DP* si_n_anis_over_2);
  DP ddlambda_Theta_XXZ (DP lambda, int nj, int nk, int parj, int park, DP* si_n_anis_over_2);



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

  // Objects in class XXX_Bethe_State carry all extra information pertaining to XXX antiferromagnet

  class XXX_Bethe_State : public Heis_Bethe_State {

  public:
    XXX_Bethe_State ();
    XXX_Bethe_State (const XXX_Bethe_State& RefState);  // copy constructor
    XXX_Bethe_State (const Heis_Chain& RefChain, int M);  // constructor to ground-state configuration
    XXX_Bethe_State (const Heis_Chain& RefChain, const Heis_Base& base);  // constructor to lowest-energy config with base

  public:
    XXX_Bethe_State& operator= (const 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
    DP String_delta ();
    void Compute_Energy ();
    void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red);

    // XXX specific functions
  public:
    bool Check_Finite_rap ();

  };

  XXX_Bethe_State Add_Particle_at_Center (const XXX_Bethe_State& RefState);
  XXX_Bethe_State Remove_Particle_at_Center (const XXX_Bethe_State& RefState);

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

  // Objects in class XXZ_gpd_Bethe_State carry all extra information pertaining to XXZ gapped antiferromagnets

  class XXZ_gpd_Bethe_State : public Heis_Bethe_State {

  public:
    Lambda sinlambda;
    Lambda coslambda;
    Lambda tanlambda;

  public:
    XXZ_gpd_Bethe_State ();
    XXZ_gpd_Bethe_State (const XXZ_gpd_Bethe_State& RefState);  // copy constructor
    XXZ_gpd_Bethe_State (const Heis_Chain& RefChain, int M);  // constructor to ground-state configuration
    XXZ_gpd_Bethe_State (const Heis_Chain& RefChain, const Heis_Base& base);  // constructor to lowest-energy config with base

  public:
    XXZ_gpd_Bethe_State& operator= (const 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]
    DP String_delta ();
    void Compute_Energy ();
    void Build_Reduced_Gaudin_Matrix (SQMat<std::complex<DP> >& Gaudin_Red);

    // XXZ_gpd specific functions
  public:

  };

  XXZ_gpd_Bethe_State Add_Particle_at_Center (const XXZ_gpd_Bethe_State& RefState);
  XXZ_gpd_Bethe_State Remove_Particle_at_Center (const XXZ_gpd_Bethe_State& RefState);


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

  // 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 Heis_Bethe_State& RefState);
  DP Particle_Hole_Excitation_Cost (char whichDSF, Heis_Bethe_State& AveragingState);

  //DP Sumrule_Factor (char whichDSF, Heis_Bethe_State& RefState, DP Chem_Pot, bool fixed_iK, int iKneeded);
  DP Sumrule_Factor (char whichDSF, Heis_Bethe_State& RefState, DP Chem_Pot, int iKmin, int iKmax);
  void Evaluate_F_Sumrule (std::string prefix, char whichDSF, const Heis_Bethe_State& RefState, DP Chem_Pot, int iKmin, int iKmax);

  std::complex<DP> ln_Sz_ME (XXZ_Bethe_State& A, XXZ_Bethe_State& B);
  std::complex<DP> ln_Smin_ME (XXZ_Bethe_State& A, XXZ_Bethe_State& B);

  std::complex<DP> ln_Sz_ME (XXX_Bethe_State& A, XXX_Bethe_State& B);
  std::complex<DP> ln_Smin_ME (XXX_Bethe_State& A, XXX_Bethe_State& B);

  // From Antoine Klauser:
  std::complex<DP> ln_Szz_ME (XXX_Bethe_State& A, XXX_Bethe_State& B);
  std::complex<DP> ln_Szm_p_Smz_ME (XXX_Bethe_State& A, XXX_Bethe_State& B);
  std::complex<DP> ln_Smm_ME (XXX_Bethe_State& A, XXX_Bethe_State& B);

  std::complex<DP> ln_Sz_ME (XXZ_gpd_Bethe_State& A, XXZ_gpd_Bethe_State& B);
  std::complex<DP> ln_Smin_ME (XXZ_gpd_Bethe_State& A, XXZ_gpd_Bethe_State& B);


  DP Compute_Matrix_Element_Contrib (char whichDSF, int iKmin, int iKmax, XXZ_Bethe_State& LeftState,
				     XXZ_Bethe_State& RefState, DP Chem_Pot, std::stringstream& DAT_outfile);
  DP Compute_Matrix_Element_Contrib (char whichDSF, int iKmin, int iKmax, XXX_Bethe_State& LeftState,
				     XXX_Bethe_State& RefState, DP Chem_Pot, std::stringstream& DAT_outfile);
  DP Compute_Matrix_Element_Contrib (char whichDSF, int iKmin, int iKmax, XXZ_gpd_Bethe_State& LeftState,
				     XXZ_gpd_Bethe_State& RefState, DP Chem_Pot, std::stringstream& DAT_outfile);

  // For geometric quench:
  std::complex<DP> ln_Overlap (XXX_Bethe_State& A, XXX_Bethe_State& B);

  void Scan_Heis_Geometric_Quench (DP Delta, int N_1, int M, long long int base_id_1, long long int type_id_1, long long int id_1,
				   int N_2, int iKmin, int iKmax, int Max_Secs, bool refine);


} // namespace ABACUS

#endif