144 lines
3.6 KiB
C++
144 lines
3.6 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: src/HEIS/Heis_Chem_Pot.cc
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Purpose: calculates the chemical potential.
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***********************************************************/
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#include "ABACUS.h"
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using namespace std;
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namespace ABACUS {
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DP Ezero (DP Delta, int N, int M)
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{
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// Returns the energy of the ground state with M down spins
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if (M < 0 || M > N/2) ABACUSerror("M out of bounds in Ezero.");
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DP E = -1.0; // sentinel value
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if (M == 0) E = N * Delta/4.0;
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else {
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Heis_Chain BD1(1.0, Delta, 0.0, N);
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Vect_INT Nrapidities_groundstate(0, BD1.Nstrings);
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Nrapidities_groundstate[0] = M;
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Heis_Base baseconfig_groundstate(BD1, Nrapidities_groundstate);
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if ((Delta > 0.0) && (Delta < 1.0)) {
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XXZ_Bethe_State groundstate(BD1, baseconfig_groundstate);
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groundstate.Compute_All(true);
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E = groundstate.E;
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}
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else if (Delta == 1.0) {
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XXX_Bethe_State groundstate(BD1, baseconfig_groundstate);
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groundstate.Compute_All(true);
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E = groundstate.E;
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}
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else if (Delta > 1.0) {
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XXZ_gpd_Bethe_State groundstate(BD1, baseconfig_groundstate);
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groundstate.Compute_All(true);
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E = groundstate.E;
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}
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else ABACUSerror("Anisotropy out of bounds in Ezero.");
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}
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return(E);
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}
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DP H_vs_M (DP Delta, int N, int M)
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{
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// Assumes dE/dM = 0 = dE_0/dM + h, with dE_0/dM = E_0(M) - E_0 (M - 1)
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DP H = 0.0;
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if (2*M == N) H = 0.0;
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else if (Delta <= 1.0) H = Ezero (Delta, N, M - 1) - Ezero (Delta, N, M);
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return(H);
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}
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DP HZmin (DP Delta, int N, int M, Vect_DP& Ezero_ref)
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{
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if (M < 0 || M > N/2 - 1) {
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cout << "M = " << M << endl;
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ABACUSerror("M out of bounds in HZmin.");
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}
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if (Ezero_ref[M] == -1.0) Ezero_ref[M] = Ezero(Delta, N, M);
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if (Ezero_ref[M + 1] == -1.0) Ezero_ref[M + 1] = Ezero(Delta, N, M + 1);
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return(Ezero_ref[M] - Ezero_ref[M + 1]);
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}
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int M_vs_H (DP Delta, int N, DP HZ)
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{
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// Returns the value of M for given field HZ
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if (HZ < 0.0) ABACUSerror("Please use a positive field in M_vs_H.");
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else if (HZ == 0.0) return(N/2);
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// Here, -1.0 is a sentinel value.
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Vect_DP Ezero(-1.0, N/2 + 1); // contains the GSE[M].
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// We look for M s.t. HZmin[M] < HZ <= HZmin[M + 1]
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int M_actual = N/4; // start somewhere in middle
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int M_step = N/8 - 1; // step
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DP HZmin_actual = 0.0;
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DP HZmax_actual = 0.0;
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bool M_found = false;
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if (HZ >= 1.0 + Delta) M_actual = 0; // saturation
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else {
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HZmin_actual = HZmin (Delta, N, M_actual, Ezero);
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HZmax_actual = HZmin (Delta, N, M_actual - 1, Ezero);
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while (!M_found) {
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if (HZmin_actual > HZ) M_actual += M_step;
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else if (HZmax_actual <= HZ) M_actual -= M_step;
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M_step = (M_step + 1)/2;
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HZmin_actual = HZmin (Delta, N, M_actual, Ezero);
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HZmax_actual = HZmin (Delta, N, M_actual - 1, Ezero);
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M_found = (HZmin_actual < HZ && HZ <= HZmax_actual);
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//cout << "M_actual = " << M_actual << "\tM_step = " << M_step
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// << "\tHZmin_actual = " << HZmin_actual << "\tHZmax_actual = " << HZmax_actual << "\tHZ = " << HZ << "\t" << M_found << endl;
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}
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}
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//cout << "M found = " << M_actual << "\tHZmax = " << Ezero[M_actual] - Ezero[M_actual + 1] << "\tHZmin = " << Ezero[M_actual - 1] - Ezero[M_actual] << endl;
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return(M_actual);
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}
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DP Chemical_Potential (const Heis_Bethe_State& AveragingState)
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{
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return(-H_vs_M (AveragingState.chain.Delta, AveragingState.chain.Nsites, AveragingState.base.Mdown)); // - sign since E_{M+1} - E_M = -H
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}
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}
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