From f13eacbc8e5ab714dd3544adab8189c313382c77 Mon Sep 17 00:00:00 2001
From: Ian Jauslin <ian.jauslin@roma1.infn.it>
Date: Wed, 22 Jul 2015 13:55:29 +0000
Subject: Support for non-commuting fields

---
 src/kondo.c | 150 +++++++++++++++++++++++++++++-------------------------------
 1 file changed, 73 insertions(+), 77 deletions(-)

(limited to 'src/kondo.c')

diff --git a/src/kondo.c b/src/kondo.c
index 39d74bb..79b7c56 100644
--- a/src/kondo.c
+++ b/src/kondo.c
@@ -29,16 +29,17 @@ limitations under the License.
 #include "definitions.cpp"
 #include "rational.h"
 
-// dimension of A, B and h (must be <10)
+// dimension of A, B, h and t (must be <10)
 #define KONDO_DIM 3
 // number of spin components
 #define KONDO_SPIN 2
 
-// offsets for indices of A, B and h
+// offsets for indices of A, B, h and t
 // order matters for symbols table
 #define KONDO_A_OFFSET 1
 #define KONDO_B_OFFSET 2
 #define KONDO_H_OFFSET 3
+#define KONDO_T_OFFSET 4
 
 // parsing modes (from parse_file.c)
 #define PP_NULL_MODE 0
@@ -193,13 +194,19 @@ int kondo_fields_table(int box_count, Char_Array* str_fields, Fields_Table* fiel
 
   //  parameters
   char_array_append_str("h:",str_fields);
+  // h
   for(i=0;i<KONDO_DIM;i++){
-    char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_H_OFFSET));
+    char_array_snprintf(str_fields, "%d,", 10*(i+10*KONDO_H_OFFSET));
+  }
+  // t
+  for(i=0;i<KONDO_DIM;i++){
+    char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_T_OFFSET));
     if(i<KONDO_DIM-1){
-      char_array_append(',',str_fields);
+      char_array_append(',', str_fields);
     }
   }
-  char_array_append('\n',str_fields);
+  char_array_append('\n', str_fields);
+
 
   // declare Fermions
   char_array_append_str("f:",str_fields);
@@ -226,6 +233,16 @@ int kondo_fields_table(int box_count, Char_Array* str_fields, Fields_Table* fiel
   }
   char_array_append('\n',str_fields);
 
+  // declare noncommuting
+  char_array_append_str("a:",str_fields);
+  for(i=0;i<KONDO_DIM;i++){
+    char_array_snprintf(str_fields, "%d", 10*(i+10*KONDO_T_OFFSET));
+    if(i<KONDO_DIM-1){
+      char_array_append(',',str_fields);
+    }
+  }
+  char_array_append('\n', str_fields);
+
   // parse fields table
   parse_input_fields(*str_fields, fields);
 
@@ -245,7 +262,7 @@ int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields){
 
   // loop over box index
   for(i=1;i<=box_count;i++){
-    // loop over letters
+    // loop over letters (A and B)
     for(j=0;j<2;j++){
       // loop over space dimension
       for(k=0;k<KONDO_DIM;k++){
@@ -255,7 +272,7 @@ int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields){
 	init_Char_Array(&tmp_str, 6);
 	char_array_snprintf(&tmp_str, "%c%d%d", letters[j], k, i);
 	// compute corresponding polynomial
-	kondo_resolve_ABh(tmp_str.str, &poly, *fields);
+	kondo_resolve_ABht(tmp_str.str, &poly, *fields);
 	free_Char_Array(tmp_str);
 	// write to output
 	polynomial_sprint(poly, str_symbols);
@@ -320,45 +337,6 @@ int kondo_symbols(Char_Array* str_symbols, int box_count, Fields_Table* fields){
   return(0);
 }
 
-// generate Kondo symbols (older method: one symbol for each scalar product)
-int kondo_symbols_scalarprod(Char_Array* str_symbols, int box_count, Fields_Table* fields){
-  int i,j,k;
-  Char_Array tmp_str;
-  Polynomial poly;
-  char letters[3]={'A','B','h'};
-
-  init_Char_Array(str_symbols, STR_SIZE);
-  char_array_snprintf(str_symbols, "#!symbols\n");
-
-  // loop over box index
-  for(i=1;i<=box_count;i++){
-    // loop over letters
-    for(j=0;j<3;j++){
-      for(k=0;k<3;k++){
-	// write index
-	char_array_snprintf(str_symbols, "%d=", 100*(10*(KONDO_A_OFFSET+j)+KONDO_A_OFFSET+k)+i);
-	// write the name of the scalar product
-	init_Char_Array(&tmp_str, 6);
-	char_array_snprintf(&tmp_str, "%c%d.%c%d", letters[j], i, letters[k], i);
-	// compute corresponding polynomial
-	kondo_resolve_scalar_prod(tmp_str.str, &poly, *fields);
-	free_Char_Array(tmp_str);
-	// write to output
-	polynomial_sprint(poly, str_symbols);
-	free_Polynomial(poly);
-	// add ,
-	if(i<box_count || j<2 || k<2){
-	  char_array_snprintf(str_symbols,",\n");
-	}
-      }
-    }
-  }
-
-  parse_input_symbols(*str_symbols, fields);
-
-  return(0);
-}
-
 
 // generate Kondo groups (groups of independent variables)
 int kondo_groups(Char_Array* str_groups, int box_count){
@@ -395,12 +373,21 @@ int kondo_groups(Char_Array* str_groups, int box_count){
 
 // generate Kondo identities
 // h_3^2=1-h_1^2-h_2^2
+// and Pauli matrices
 int kondo_identities(Char_Array* str_identities){
   int i;
 
   init_Char_Array(str_identities,STR_SIZE);
   char_array_snprintf(str_identities, "#!identities\n");
 
+  // Pauli matrices
+  for(i=0;i<KONDO_DIM;i++){
+    char_array_snprintf(str_identities,"[f%d][f%d]=(1),\n",10*(10*KONDO_T_OFFSET+i),10*(10*KONDO_T_OFFSET+i));
+    char_array_snprintf(str_identities,"[f%d][f%d]=(s{-1})[f%d],\n",10*(10*KONDO_T_OFFSET+i),10*(10*KONDO_T_OFFSET+(i+1)%3),10*(10*KONDO_T_OFFSET+(i+2)%3));
+    char_array_snprintf(str_identities,"[f%d][f%d]=((-1)s{-1})[f%d],\n",10*(10*KONDO_T_OFFSET+(i+2)%3),10*(10*KONDO_T_OFFSET+(i+1)%3),10*(10*KONDO_T_OFFSET+i));
+  }
+
+  // h
   char_array_snprintf(str_identities, "[f%d][f%d]=(1)",10*(KONDO_DIM-1+10*KONDO_H_OFFSET),10*(KONDO_DIM-1+10*KONDO_H_OFFSET));
   for(i=0;i<KONDO_DIM-1;i++){
     char_array_snprintf(str_identities, "+(-1)[f%d][f%d]",10*(i+10*KONDO_H_OFFSET),10*(i+10*KONDO_H_OFFSET));
@@ -809,11 +796,10 @@ int parse_kondo_polynomial_str(char* str_polynomial, Polynomial* output, Fields_
 	  if(tmp_poly.length>0){
 	    for(i=0;i<tmp_poly.length;i++){
 	      if(mode==PP_FIELD_SCALAR_MODE){
-		if(offset1!=KONDO_H_OFFSET || offset2!=KONDO_H_OFFSET){
-		  int_array_append(1000*(10*offset1+offset2)+index, tmp_poly.monomials+i);
-		}
+		int_array_append(1000*(10*offset1+offset2)+index, tmp_poly.monomials+i);
 	      }
 	      else{
+		// vector product
 		int_array_append(100*(100*KONDO_A_OFFSET+10*KONDO_B_OFFSET+KONDO_H_OFFSET)+index, tmp_poly.monomials+i);
 	      }
 	    }
@@ -822,28 +808,15 @@ int parse_kondo_polynomial_str(char* str_polynomial, Polynomial* output, Fields_
 	  else{
 	    init_Int_Array(&tmp_monomial, MONOMIAL_SIZE);
 	    if(mode==PP_FIELD_SCALAR_MODE){
-	      if(offset1!=KONDO_H_OFFSET || offset2!=KONDO_H_OFFSET){
-		int_array_append(1000*(10*offset1+offset2)+index, &tmp_monomial);
-	      }
+	      int_array_append(1000*(10*offset1+offset2)+index, &tmp_monomial);
 	    }
 	    else{
+	      // vector product
 	      int_array_append(100*(100*KONDO_A_OFFSET+10*KONDO_B_OFFSET+KONDO_H_OFFSET)+index, &tmp_monomial);
 	    }
 	    init_Int_Array(&dummy_factor, 1);
 	    polynomial_append_noinit(tmp_monomial, dummy_factor, number_one(), &tmp_poly);
 	  }
-	  /* // older method in which a scalar product was expanded in A, B and h
-	  // resolve scalar product
-	  kondo_resolve_scalar_prod_symbols(buffer, &scalar_prod_poly);
-	  // add to tmp_poly
-	  if(tmp_poly.length==0){
-	    polynomial_concat(scalar_prod_poly,&tmp_poly);
-	  }
-	  else{
-	    polynomial_prod_chain(scalar_prod_poly,&tmp_poly,fields);
-	  }
-	  free_Polynomial(scalar_prod_poly);
-	  */
 	}
 	// switch back to null mode
 	mode=PP_NULL_MODE;
@@ -941,10 +914,10 @@ int parse_kondo_polynomial(Char_Array kondo_polynomial_str, Polynomial* polynomi
 }
 
 
-// read Aij, Bij, hi where i is a space dimension and j is a box index
-int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
+// read Aij, Bij, hi, ti where i is a space dimension and j is a box index
+int kondo_resolve_ABht(char* str, Polynomial* output, Fields_Table fields){
   char* ptr;
-  // offset (A,B or H)
+  // offset (A,B, H or T)
   int offset=-1;
   // dimension
   int dim=-1;
@@ -978,6 +951,9 @@ int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
     case 'h':
       offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset=KONDO_T_OFFSET;
+      break;
     default:
       // set index if dim was already set
       if(dim>=0){
@@ -1001,8 +977,8 @@ int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
     }
   }
 
-  // h's
-  if(offset==KONDO_H_OFFSET){
+  // h's and t's
+  if(offset==KONDO_H_OFFSET || offset==KONDO_T_OFFSET){
     // external field
     init_Int_Array(&monomial,1);
     init_Int_Array(&factor,1);
@@ -1062,7 +1038,7 @@ int kondo_resolve_ABh(char* str, Polynomial* output, Fields_Table fields){
 // read a Kondo scalar product (generalized to vector products as well)
 int kondo_resolve_scalar_prod(char* str, Polynomial* output, Fields_Table fields){
   char* ptr;
-  // offset of each term (A,B or H)
+  // offset of each term (A,B,H or T)
   int offset=-1;
   // index of each term (0,...,box_count)
   int index=0;
@@ -1091,6 +1067,9 @@ int kondo_resolve_scalar_prod(char* str, Polynomial* output, Fields_Table fields
     case 'h':
       offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset=KONDO_T_OFFSET;
+      break;
 
     // scalar product
     case '.':
@@ -1195,8 +1174,8 @@ int kondo_polynomial_vector(int offset, int index, Polynomial (*polys)[3], Field
     init_Polynomial((*polys)+i,POLY_SIZE);
   }
 
-  // h's
-  if(offset==KONDO_H_OFFSET){
+  // h's and t's
+  if(offset==KONDO_H_OFFSET || offset==KONDO_T_OFFSET){
     // construct every component field
     for(i=0;i<KONDO_DIM;i++){
       // external field
@@ -1261,7 +1240,7 @@ int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output){
   char* ptr;
   // first or second term
   int term=0;
-  // offset of each term (A,B or H)
+  // offset of each term (A,B,H or T)
   int offset[2];
   // index of each term (0,...,box_count)
   int index[2]={0,0};
@@ -1289,6 +1268,9 @@ int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output){
     case 'h':
       offset[term]=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset[term]=KONDO_T_OFFSET;
+      break;
     // switch term
     case '.':
       term=1-term;
@@ -1304,13 +1286,13 @@ int kondo_resolve_scalar_prod_symbols(char* str, Polynomial* output){
     init_Int_Array(&monomial,2);
     init_Int_Array(&factor, 1);
 
-    if(offset[0]==KONDO_H_OFFSET){
+    if(offset[0]==KONDO_H_OFFSET || offset[0]==KONDO_T_OFFSET){
       int_array_append(10*(10*offset[0]+i)+index[0], &monomial);
     }
     else{
       int_array_append(100*(10*offset[0]+i)+index[0], &monomial);
     }
-    if(offset[1]==KONDO_H_OFFSET){
+    if(offset[1]==KONDO_H_OFFSET || offset[1]==KONDO_T_OFFSET){
       int_array_append(10*(10*offset[1]+i)+index[1], &monomial);
     }
     else{
@@ -1344,6 +1326,9 @@ int get_offset_index(char* str, int* offset, int* index){
     case 'h':
       *offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      *offset=KONDO_T_OFFSET;
+      break;
     default:
       // char to int
       *index=*ptr-'0';
@@ -1378,6 +1363,9 @@ int get_offsets_index(char* str, int* offset1, int* offset2, int* index){
     case 'h':
       offset[term]=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset[term]=KONDO_T_OFFSET;
+      break;
     // switch term
     case '.':
       term=1-term;
@@ -1391,6 +1379,11 @@ int get_offsets_index(char* str, int* offset1, int* offset2, int* index){
   *offset1=offset[0];
   *offset2=offset[1];
 
+  // if no A's or B's, then index=0
+  if((offset[0]==KONDO_H_OFFSET || offset[0]==KONDO_T_OFFSET) && (offset[1]==KONDO_H_OFFSET || offset[1]==KONDO_T_OFFSET)){
+    *index=0;
+  }
+
   return(0);
 }
 
@@ -1429,6 +1422,9 @@ int get_symbol_index(char* str){
     case 'h':
       offset=KONDO_H_OFFSET;
       break;
+    case 't':
+      offset=KONDO_T_OFFSET;
+      break;
     default:
       // set index if dim was already set
       if(dim>=0){
@@ -1443,8 +1439,8 @@ int get_symbol_index(char* str){
   if(offset==-1){
     return(-1);
   }
-  // no symbol for h
-  if(offset==KONDO_H_OFFSET){
+  // no symbol for h or t
+  if(offset==KONDO_H_OFFSET || offset==KONDO_T_OFFSET){
     return(10*(10*offset+dim));
   }
   else{
-- 
cgit v1.2.3-70-g09d2