Import ABACUS++G_8 code; cleanup files; new README
This commit is contained in:
J.-S. Caux
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#include "JSC.h"
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using namespace JSC;
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namespace JSC {
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inline complex<DP> ln_Fn_F (ODSLF_XXZ_Bethe_State& B, int k, int beta, int b)
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{
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complex<DP> ans = 0.0;
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complex<DP> prod_temp = 1.0;
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int counter = 0;
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int arg = 0;
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int absarg = 0;
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int par_comb_1, par_comb_2;
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for (int j = 0; j < B.chain.Nstrings; ++j) {
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par_comb_1 = B.chain.par[j] == B.chain.par[k] ? 1 : 0;
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par_comb_2 = B.chain.par[k] == B.chain.par[j] ? 0 : B.chain.par[k];
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for (int alpha = 0; alpha < B.base.Nrap[j]; ++alpha) {
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for (int a = 1; a <= B.chain.Str_L[j]; ++a) {
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if (!((j == k) && (alpha == beta) && (a == b))) {
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arg = B.chain.Str_L[j] - B.chain.Str_L[k] - 2 * (a - b);
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absarg = abs(arg);
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/*
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prod_temp *= 0.5 *
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((B.sinhlambda[j][alpha] * B.coshlambda[k][beta] - B.coshlambda[j][alpha] * B.sinhlambda[k][beta])
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* (B.chain.co_n_anis_over_2[absarg] * (1.0 + B.chain.par[j] * B.chain.par[k])
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- sgn_int(arg) * B.chain.si_n_anis_over_2[absarg] * (B.chain.par[k] - B.chain.par[j]))
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+ II * (B.coshlambda[j][alpha] * B.coshlambda[k][beta] - B.sinhlambda[j][alpha] * B.sinhlambda[k][beta])
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* (sgn_int(arg)
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* B.chain.si_n_anis_over_2[absarg] * (1.0 + B.chain.par[j] * B.chain.par[k])
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+ B.chain.co_n_anis_over_2[absarg] * (B.chain.par[k] - B.chain.par[j])) );
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*/
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prod_temp *= ((B.sinhlambda[j][alpha] * B.coshlambda[k][beta] - B.coshlambda[j][alpha] * B.sinhlambda[k][beta])
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* (B.chain.co_n_anis_over_2[absarg] * par_comb_1 - sgn_int(arg) * B.chain.si_n_anis_over_2[absarg] * par_comb_2)
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+ II * (B.coshlambda[j][alpha] * B.coshlambda[k][beta] - B.sinhlambda[j][alpha] * B.sinhlambda[k][beta])
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* (sgn_int(arg) * B.chain.si_n_anis_over_2[absarg] * par_comb_1 + B.chain.co_n_anis_over_2[absarg] * par_comb_2));
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}
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if (counter++ > 100) { // we do at most 100 products before taking a log
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ans += log(prod_temp);
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prod_temp = 1.0;
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counter = 0;
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}
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}}}
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return(ans + log(prod_temp));
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}
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inline complex<DP> ln_Fn_G (ODSLF_XXZ_Bethe_State& A, ODSLF_XXZ_Bethe_State& B, int k, int beta, int b)
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{
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complex<DP> ans = 0.0;
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complex<DP> prod_temp = 1.0;
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int counter = 0;
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int arg = 0;
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int absarg = 0;
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int par_comb_1, par_comb_2;
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for (int j = 0; j < A.chain.Nstrings; ++j) {
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par_comb_1 = A.chain.par[j] == B.chain.par[k] ? 1 : 0;
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par_comb_2 = B.chain.par[k] == A.chain.par[j] ? 0 : B.chain.par[k];
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for (int alpha = 0; alpha < A.base.Nrap[j]; ++alpha) {
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for (int a = 1; a <= A.chain.Str_L[j]; ++a) {
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arg = A.chain.Str_L[j] - B.chain.Str_L[k] - 2 * (a - b);
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absarg = abs(arg);
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/*
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prod_temp *= 0.5 *
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((A.sinhlambda[j][alpha] * B.coshlambda[k][beta] - A.coshlambda[j][alpha] * B.sinhlambda[k][beta])
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* (A.chain.co_n_anis_over_2[absarg] * (1.0 + A.chain.par[j] * B.chain.par[k])
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- sgn_int(arg) * A.chain.si_n_anis_over_2[absarg] * (B.chain.par[k] - A.chain.par[j]))
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+ II * (A.coshlambda[j][alpha] * B.coshlambda[k][beta] - A.sinhlambda[j][alpha] * B.sinhlambda[k][beta])
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* (sgn_int(arg) * A.chain.si_n_anis_over_2[absarg] * (1.0 + A.chain.par[j] * B.chain.par[k])
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+ A.chain.co_n_anis_over_2[absarg] * (B.chain.par[k] - A.chain.par[j])) );
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*/
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prod_temp *= ((A.sinhlambda[j][alpha] * B.coshlambda[k][beta] - A.coshlambda[j][alpha] * B.sinhlambda[k][beta])
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* (A.chain.co_n_anis_over_2[absarg] * par_comb_1 - sgn_int(arg) * A.chain.si_n_anis_over_2[absarg] * par_comb_2)
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+ II * (A.coshlambda[j][alpha] * B.coshlambda[k][beta] - A.sinhlambda[j][alpha] * B.sinhlambda[k][beta])
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* (sgn_int(arg) * A.chain.si_n_anis_over_2[absarg] * par_comb_1 + A.chain.co_n_anis_over_2[absarg] * par_comb_2));
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if (counter++ > 100) { // we do at most 100 products before taking a log
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ans += log(prod_temp);
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prod_temp = 1.0;
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counter = 0;
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}
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}}}
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return(ans + log(prod_temp));
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}
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inline complex<DP> Fn_K (ODSLF_XXZ_Bethe_State& A, int j, int alpha, int a, ODSLF_XXZ_Bethe_State& B, int k, int beta, int b)
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{
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int arg1 = A.chain.Str_L[j] - B.chain.Str_L[k] - 2 * (a - b);
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int absarg1 = abs(arg1);
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int arg2 = arg1 + 2;
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int absarg2 = abs(arg2);
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return(4.0/(
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((A.sinhlambda[j][alpha] * B.coshlambda[k][beta] - A.coshlambda[j][alpha] * B.sinhlambda[k][beta])
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* (A.chain.co_n_anis_over_2[absarg1] * (1.0 + A.chain.par[j] * B.chain.par[k])
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- sgn_int(arg1) * A.chain.si_n_anis_over_2[absarg1] * (B.chain.par[k] - A.chain.par[j]))
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+ II * (A.coshlambda[j][alpha] * B.coshlambda[k][beta] - A.sinhlambda[j][alpha] * B.sinhlambda[k][beta])
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* (sgn_int(arg1) * A.chain.si_n_anis_over_2[absarg1] * (1.0 + A.chain.par[j] * B.chain.par[k])
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+ A.chain.co_n_anis_over_2[absarg1] * (B.chain.par[k] - A.chain.par[j])) )
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*
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((A.sinhlambda[j][alpha] * B.coshlambda[k][beta] - A.coshlambda[j][alpha] * B.sinhlambda[k][beta])
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* (A.chain.co_n_anis_over_2[absarg2] * (1.0 + A.chain.par[j] * B.chain.par[k])
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- sgn_int(arg2) * A.chain.si_n_anis_over_2[absarg2] * (B.chain.par[k] - A.chain.par[j]))
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+ II * (A.coshlambda[j][alpha] * B.coshlambda[k][beta] - A.sinhlambda[j][alpha] * B.sinhlambda[k][beta])
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* (sgn_int(arg2) * A.chain.si_n_anis_over_2[absarg2] * (1.0 + A.chain.par[j] * B.chain.par[k])
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+ A.chain.co_n_anis_over_2[absarg2] * (B.chain.par[k] - A.chain.par[j])) )
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));
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}
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inline complex<DP> Fn_L (ODSLF_XXZ_Bethe_State& A, int j, int alpha, int a, ODSLF_XXZ_Bethe_State& B, int k, int beta, int b)
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{
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return (sinh(2.0 * (A.lambda[j][alpha] - B.lambda[k][beta]
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+ 0.5 * II * B.chain.anis * (A.chain.Str_L[j] - B.chain.Str_L[k] - 2.0 * (a - b - 0.5))
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+ 0.25 * II * PI * complex<DP>(-A.chain.par[j] + B.chain.par[k])))
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* pow(Fn_K (A, j, alpha, a, B, k, beta, b), 2.0));
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}
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complex<DP> ln_Sz_ME (ODSLF_XXZ_Bethe_State& A, ODSLF_XXZ_Bethe_State& B)
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{
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// This function returns the natural log of the S^z operator matrix element.
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// The A and B states can contain strings.
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// Check that the two states refer to the same XXZ_Chain
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if (A.chain != B.chain) JSCerror("Incompatible ODSLF_XXZ_Chains in Sz matrix element.");
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// Check that A and B are compatible: same Mdown
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if (A.base.Mdown != B.base.Mdown) JSCerror("Incompatible Mdown between the two states in Sz matrix element!");
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// Compute the sinh and cosh of rapidities
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A.Compute_sinhlambda();
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A.Compute_coshlambda();
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B.Compute_sinhlambda();
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B.Compute_coshlambda();
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// Some convenient arrays
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ODSLF_Lambda re_ln_Fn_F_B_0(B.chain, B.base);
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ODSLF_Lambda im_ln_Fn_F_B_0(B.chain, B.base);
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ODSLF_Lambda re_ln_Fn_G_0(B.chain, B.base);
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ODSLF_Lambda im_ln_Fn_G_0(B.chain, B.base);
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ODSLF_Lambda re_ln_Fn_G_2(B.chain, B.base);
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ODSLF_Lambda im_ln_Fn_G_2(B.chain, B.base);
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complex<DP> ln_prod1 = 0.0;
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complex<DP> ln_prod2 = 0.0;
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complex<DP> ln_prod3 = 0.0;
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complex<DP> ln_prod4 = 0.0;
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for (int i = 0; i < A.chain.Nstrings; ++i)
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for (int alpha = 0; alpha < A.base.Nrap[i]; ++alpha)
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for (int a = 1; a <= A.chain.Str_L[i]; ++a)
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ln_prod1 += log(norm(sinh(A.lambda[i][alpha] + 0.5 * II * A.chain.anis * (A.chain.Str_L[i] + 1.0 - 2.0 * a - 1.0)
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+ 0.25 * II * PI * (1.0 - A.chain.par[i]))));
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for (int i = 0; i < B.chain.Nstrings; ++i)
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for (int alpha = 0; alpha < B.base.Nrap[i]; ++alpha)
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for (int a = 1; a <= B.chain.Str_L[i]; ++a)
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if (norm(sinh(B.lambda[i][alpha] + 0.5 * II * B.chain.anis * (B.chain.Str_L[i] + 1.0 - 2.0 * a - 1.0)
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+ 0.25 * II * PI * (1.0 - B.chain.par[i]))) > 100.0 * MACHINE_EPS_SQ)
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ln_prod2 += log(norm(sinh(B.lambda[i][alpha] + 0.5 * II * B.chain.anis * (B.chain.Str_L[i] + 1.0 - 2.0 * a - 1.0)
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+ 0.25 * II * PI * (1.0 - B.chain.par[i]))));
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// Define the F ones earlier...
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for (int j = 0; j < B.chain.Nstrings; ++j) {
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for (int alpha = 0; alpha < B.base.Nrap[j]; ++alpha) {
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re_ln_Fn_F_B_0[j][alpha] = real(ln_Fn_F(B, j, alpha, 0));
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im_ln_Fn_F_B_0[j][alpha] = imag(ln_Fn_F(B, j, alpha, 0));
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re_ln_Fn_G_0[j][alpha] = real(ln_Fn_G(A, B, j, alpha, 0));
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im_ln_Fn_G_0[j][alpha] = imag(ln_Fn_G(A, B, j, alpha, 0));
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re_ln_Fn_G_2[j][alpha] = real(ln_Fn_G(A, B, j, alpha, 2));
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im_ln_Fn_G_2[j][alpha] = imag(ln_Fn_G(A, B, j, alpha, 2));
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}
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}
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DP logabssinzeta = log(abs(sin(A.chain.anis)));
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// Define regularized products in prefactors
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for (int j = 0; j < A.chain.Nstrings; ++j)
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for (int alpha = 0; alpha < A.base.Nrap[j]; ++alpha)
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for (int a = 1; a <= A.chain.Str_L[j]; ++a) {
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ln_prod3 += ln_Fn_F (A, j, alpha, a - 1);
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}
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ln_prod3 -= A.base.Mdown * log(abs(sin(A.chain.anis)));
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for (int k = 0; k < B.chain.Nstrings; ++k)
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for (int beta = 0; beta < B.base.Nrap[k]; ++beta)
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for (int b = 1; b <= B.chain.Str_L[k]; ++b) {
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if (b == 1) ln_prod4 += re_ln_Fn_F_B_0[k][beta];
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else if (b > 1) ln_prod4 += ln_Fn_F(B, k, beta, b - 1);
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}
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ln_prod4 -= B.base.Mdown * log(abs(sin(B.chain.anis)));
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// Now proceed to build the Hm2P matrix
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SQMat_CX Hm2P(0.0, A.base.Mdown);
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int index_a = 0;
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int index_b = 0;
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complex<DP> sum1 = 0.0;
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complex<DP> sum2 = 0.0;
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complex<DP> prod_num = 0.0;
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complex<DP> Fn_K_0_G_0 = 0.0;
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complex<DP> Prod_powerN = 0.0;
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complex<DP> Fn_K_1_G_2 = 0.0;
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complex<DP> two_over_A_sinhlambda_sq_plus_sinzetaover2sq;
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for (int j = 0; j < A.chain.Nstrings; ++j) {
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for (int alpha = 0; alpha < A.base.Nrap[j]; ++alpha) {
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for (int a = 1; a <= A.chain.Str_L[j]; ++a) {
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index_b = 0;
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two_over_A_sinhlambda_sq_plus_sinzetaover2sq = 2.0/((sinh(A.lambda[j][alpha] + 0.5 * II * A.chain.anis * (A.chain.Str_L[j] + 1.0 - 2.0 * a)
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+ 0.25 * II * PI * (1.0 - A.chain.par[j])))
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* (sinh(A.lambda[j][alpha] + 0.5 * II * A.chain.anis * (A.chain.Str_L[j] + 1.0 - 2.0 * a)
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+ 0.25 * II * PI * (1.0 - A.chain.par[j])))
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+ pow(sin(0.5*A.chain.anis), 2.0));
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for (int k = 0; k < B.chain.Nstrings; ++k) {
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for (int beta = 0; beta < B.base.Nrap[k]; ++beta) {
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for (int b = 1; b <= B.chain.Str_L[k]; ++b) {
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if (B.chain.Str_L[k] == 1) {
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// use simplified code for one-string here: original form of Hm2P matrix
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Fn_K_0_G_0 = Fn_K (A, j, alpha, a, B, k, beta, 0) *
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exp(re_ln_Fn_G_0[k][beta] + II * im_ln_Fn_G_0[k][beta] - re_ln_Fn_F_B_0[k][beta] + logabssinzeta);
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Fn_K_1_G_2 = Fn_K (A, j, alpha, a, B, k, beta, 1) *
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exp(re_ln_Fn_G_2[k][beta] + II * im_ln_Fn_G_2[k][beta] - re_ln_Fn_F_B_0[k][beta] + logabssinzeta);
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Prod_powerN = pow( B.chain.par[k] == 1 ?
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(B.sinhlambda[k][beta] * B.chain.co_n_anis_over_2[1] + II * B.coshlambda[k][beta] * B.chain.si_n_anis_over_2[1])
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/(B.sinhlambda[k][beta] * B.chain.co_n_anis_over_2[1] - II * B.coshlambda[k][beta] * B.chain.si_n_anis_over_2[1])
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:
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(B.coshlambda[k][beta] * B.chain.co_n_anis_over_2[1] + II * B.sinhlambda[k][beta] * B.chain.si_n_anis_over_2[1])
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/(B.coshlambda[k][beta] * B.chain.co_n_anis_over_2[1] - II * B.sinhlambda[k][beta] * B.chain.si_n_anis_over_2[1])
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, complex<DP> (B.chain.Nsites));
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Hm2P[index_a][index_b] = Fn_K_0_G_0 - (-1.0 + 2.0 * (B.base.Mdown % 2)) * // MODIF from XXZ
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Prod_powerN * Fn_K_1_G_2 - two_over_A_sinhlambda_sq_plus_sinzetaover2sq
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* exp(II*im_ln_Fn_F_B_0[k][beta] + logabssinzeta);
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}
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else {
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if (b <= B.chain.Str_L[k] - 1) Hm2P[index_a][index_b] = Fn_K(A, j, alpha, a, B, k, beta, b);
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else if (b == B.chain.Str_L[k]) {
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Vect_CX ln_FunctionF(B.chain.Str_L[k] + 2);
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for (int i = 0; i < B.chain.Str_L[k] + 2; ++i) ln_FunctionF[i] = ln_Fn_F (B, k, beta, i);
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Vect_CX ln_FunctionG(B.chain.Str_L[k] + 2);
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for (int i = 0; i < B.chain.Str_L[k] + 2; ++i) ln_FunctionG[i] = ln_Fn_G (A, B, k, beta, i);
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sum1 = 0.0;
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sum1 += Fn_K (A, j, alpha, a, B, k, beta, 0) * exp(ln_FunctionG[0] + ln_FunctionG[1] - ln_FunctionF[0] - ln_FunctionF[1]);
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sum1 += (-1.0 + 2.0 * (B.base.Mdown % 2)) * // MODIF from XXZ
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Fn_K (A, j, alpha, a, B, k, beta, B.chain.Str_L[k])
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* exp(ln_FunctionG[B.chain.Str_L[k]] + ln_FunctionG[B.chain.Str_L[k] + 1]
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- ln_FunctionF[B.chain.Str_L[k]] - ln_FunctionF[B.chain.Str_L[k] + 1]);
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for (int jsum = 1; jsum < B.chain.Str_L[k]; ++jsum)
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sum1 -= Fn_L (A, j, alpha, a, B, k, beta, jsum) *
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exp(ln_FunctionG[jsum] + ln_FunctionG[jsum + 1] - ln_FunctionF[jsum] - ln_FunctionF[jsum + 1]);
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sum2 = 0.0;
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for (int jsum = 1; jsum <= B.chain.Str_L[k]; ++jsum) sum2 += exp(ln_FunctionG[jsum] - ln_FunctionF[jsum]);
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prod_num = exp(II * im_ln_Fn_F_B_0[k][beta] + ln_FunctionF[1] - ln_FunctionG[B.chain.Str_L[k]] + logabssinzeta);
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for (int jsum = 2; jsum <= B.chain.Str_L[k]; ++jsum)
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prod_num *= exp(ln_FunctionG[jsum] - real(ln_FunctionF[jsum - 1]) + logabssinzeta);
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// include all string contributions F_B_0 in this term
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|
||||
Hm2P[index_a][index_b] = prod_num * (sum1 - sum2 * two_over_A_sinhlambda_sq_plus_sinzetaover2sq);
|
||||
|
||||
} // else if (b == B.chain.Str_L[k])
|
||||
} // else
|
||||
|
||||
index_b++;
|
||||
}}} // sums over k, beta, b
|
||||
index_a++;
|
||||
}}} // sums over j, alpha, a
|
||||
|
||||
DP re_ln_det = real(lndet_LU_CX_dstry(Hm2P));
|
||||
|
||||
complex<DP> ln_ME_sq = log(0.25 * A.chain.Nsites) + real(ln_prod1 - ln_prod2) - real(ln_prod3) + real(ln_prod4)
|
||||
+ 2.0 * /*real(lndet_LU_CX_dstry(Hm2P))*/ re_ln_det - A.lnnorm - B.lnnorm;
|
||||
|
||||
//cout << endl << ln_prod1 << "\t" << ln_prod2 << "\t" << ln_prod3 << "\t" << ln_prod4 << "\t" << A.lnnorm << "\t" << B.lnnorm
|
||||
// << "\t" << re_ln_det << "\t" << ln_ME_sq << endl;
|
||||
|
||||
//return(ln_ME_sq);
|
||||
return(0.5 * ln_ME_sq); // Return ME, not MEsq
|
||||
|
||||
}
|
||||
|
||||
} // namespace JSC
|
||||
Reference in New Issue
Block a user