146 rader
5.7 KiB
C++
146 rader
5.7 KiB
C++
/**********************************************************
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This software is part of J.-S. Caux's ABACUS. library.
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Copyright (c) J.-S. Caux.
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-----------------------------------------------------------
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File: ABACUS_TBA.h
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Purpose: Thermodynamic Bethe Ansatz general functions
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***********************************************************/
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#ifndef ABACUS_TBA_H
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#define ABACUS_TBA_H
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#include "ABACUS.h"
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namespace ABACUS {
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struct Root_Density {
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int Npts; // how many points are used to describe each function
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DP lambdamax; // what the largest rapidity is
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Vect_DP lambda; // rapidity vector
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Vect_DP dlambda; // differential element
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Vect_DP value; // the root density itself
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Vect_DP prev_value; // results of previous iteration
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DP diff; // relative differences with previous iteration
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bool value_infty_set; // boolean, true if asymptotic value set
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DP value_infty; // asymptotic value, computed analytically
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Root_Density ();
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Root_Density (int Npts_ref, DP lambdamax_ref);
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Root_Density& operator= (const Root_Density& RefDensity);
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void Save (const char* outfile_Cstr);
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DP Return_Value (DP lambda_ref); // evaluates the function for any argument using linear interpolation
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void Set_Asymptotics (DP value_infty_ref); // sets value for lambda >= lambdamax
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Root_Density Compress_and_Match_Densities (DP comp_factor); // returns a Root_Density with fewer points
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};
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struct Root_Density_Set {
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int ntypes;
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Vect<Root_Density> epsilon;
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int Npts_total; // sum of all Npts of epsilon's
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DP diff; // sum of diff's of the epsilon's
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Root_Density_Set ();
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Root_Density_Set (int ntypes_ref, int Npts_ref, DP lambdamax_ref);
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Root_Density_Set (int ntypes_ref, Vect_INT Npts_ref, Vect_DP lambdamax_ref);
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Root_Density_Set& operator= (const Root_Density_Set& RefSet);
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void Insert_new_function (DP asymptotic_value);
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void Extend_limits (Vect<bool> need_to_extend_limit);
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void Insert_new_points (Vect<Vect<bool> > need_new_point_around);
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DP Return_Value (int n_ref, DP lambda_ref); // returns a value, no matter what.
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Root_Density_Set Return_Compressed_and_Matched_Set (DP comp_factor);
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void Match_Densities (Root_Density_Set& RefSet);
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void Save (const char* outfile_Cstr);
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};
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struct LiebLin_TBA_Solution {
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DP c_int;
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DP mu;
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DP kBT;
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DP nbar;
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DP ebar; // mean energy, \int d\lambda \lambda^2 \rho (\lambda)
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DP sbar; // entropy per unit length
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Root_Density epsilon;
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Root_Density depsilon_dmu;
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Root_Density rho;
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Root_Density rhoh;
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LiebLin_TBA_Solution (DP c_int_ref, DP mu_ref, DP kBT_ref, DP req_diff, int Max_Secs);
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};
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// Functions defined in TBA_LiebLin.cc
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Root_Density LiebLin_rho_GS (DP c_int, DP k_F, DP lambdamax, int Npts, DP req_prec);
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DP Density_GS (Root_Density& rho_GS);
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DP k_F_given_n (DP c_int, DP n, DP lambdamax, int Npts, DP req_prec);
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Root_Density LiebLin_Z_GS (DP c_int, DP k_F, DP lambdamax, int Npts, DP req_prec);
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Root_Density LiebLin_Fbackflow_GS (DP c_int, DP k_F, DP lambdamax, DP lambda, int Npts, DP req_prec);
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// epsilon for a given mu:
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Root_Density LiebLin_epsilon_TBA (DP c_int, DP mu, DP kBT, DP req_diff, int Max_Secs);
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// depsilon/dmu for a given mu:
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Root_Density LiebLin_depsilon_dmu_TBA (DP c_int, DP mu, DP kBT, DP req_diff, int Max_Secs, const Root_Density& epsilon);
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Root_Density LiebLin_rho_TBA (DP kBT, const Root_Density& epsilon, const Root_Density& depsilon_dmu);
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Root_Density LiebLin_rhoh_TBA (DP kBT, const Root_Density& epsilon, const Root_Density& depsilon_dmu);
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DP LiebLin_nbar_TBA (const Root_Density& rho);
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DP LiebLin_ebar_TBA (const Root_Density& rho);
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DP LiebLin_sbar_TBA (const Root_Density& rho, const Root_Density& rhoh);
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LiebLin_TBA_Solution LiebLin_TBA_Solution_fixed_nbar (DP c_int, DP nbar_required, DP kBT, DP req_diff, int Max_Secs);
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LiebLin_TBA_Solution LiebLin_TBA_Solution_fixed_nbar_ebar (DP c_int, DP nbar_required, DP ebar_required, DP req_diff, int Max_Secs);
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LiebLin_Bethe_State Discretized_LiebLin_Bethe_State (DP c_int, DP L, int N, const Root_Density& rho);
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// Functions defined in TBA_XXZ.cc
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DP XXZ_phi1_kernel (DP zeta, DP lambda);
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DP XXZ_phi2_kernel (DP zeta, DP lambda);
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DP XXZ_a1_kernel (DP sinzeta, DP coszeta, DP lambda);
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DP XXZ_da1dlambda_kernel (DP sinzeta, DP coszeta, DP lambda);
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DP XXZ_a2_kernel (DP sin2zeta, DP cos2zeta, DP lambda);
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Root_Density XXZ_rhotot_GS (DP Delta, DP B, DP lambdamax, int Npts, DP req_prec);
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DP Return_GS_Sz_tot_value (DP B, Root_Density& rhotot_GS);
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Root_Density XXZ_eps_GS (DP Delta, DP Hz, DP lambdamax, int Npts, DP req_prec);
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Root_Density XXZ_depsdlambda_GS (DP Delta, DP B, DP lambdamax, int Npts, DP req_prec);
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Root_Density XXZ_b2BB_lambda_B (DP Delta, DP B, DP lambdamax, int Npts, DP req_prec);
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Root_Density XXZ_b2BB_lambda_lambdap (DP Delta, DP B, DP lambdap, DP lambdamax, int Npts, DP req_prec);
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Root_Density XXZ_Kbackflow_GS (DP Delta, DP B, DP lambdamax, DP lambda_p, DP lambda_h, int Npts, DP req_prec);
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Root_Density XXZ_Fbackflow_GS (DP Delta, DP B, DP lambdamax, DP lambda_p, DP lambda_h, int Npts, DP req_prec);
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Root_Density XXZ_Z_GS (DP Delta, DP B, DP lambdamax, int Npts, DP req_prec);
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// Defined in TBA_2CBG.cc:
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struct TBA_Data_2CBG {
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DP c_int;
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DP mu;
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DP Omega;
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DP kBT;
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DP f; // Gibbs free energy
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DP n1; // first population
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DP n2; // second population
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};
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// Defined in src/TBA_2CBG.cc:
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TBA_Data_2CBG Solve_2CBG_TBAE_via_refinements (DP c_int, DP mu, DP Omega, DP kBT, int Max_Secs, bool Save_data);
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// Defined in src/TBA_2CBG.cc:
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void Scan_2CBG_TBAE (DP c_int, DP mu_min, DP mu_max, int Nmu, DP Omega_min, DP Omega_max, int NOmega,
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DP kBT_min, DP kBT_max, int NkBT, int Max_Secs);
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} // namespace ABACUS
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#endif
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