File: ising.c

package info (click to toggle)
libquantum 1.1.1-4
  • links: PTS, VCS
  • area: main
  • in suites: stretch
  • size: 1,136 kB
  • ctags: 279
  • sloc: sh: 7,711; ansic: 3,849; makefile: 243
file content (182 lines) | stat: -rw-r--r-- 3,245 bytes parent folder | download | duplicates (3)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
/* ising.c: Calculate the ground state of the transverse field Ising model

   Copyright 2013 Bjoern Butscher, Hendrik Weimer

   This file is part of libquantum

   libquantum is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published
   by the Free Software Foundation; either version 3 of the License,
   or (at your option) any later version.

   libquantum is distributed in the hope that it will be useful, but
   WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
   General Public License for more details.

   You should have received a copy of the GNU General Public License
   along with libquantum; if not, write to the Free Software
   Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
   MA 02110-1301, USA

*/

#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include <math.h>

#include <quantum.h>

quantum_reg *hreg;
int N;
double g;
int *V;

quantum_reg H(MAX_UNSIGNED i, double t)
{
  quantum_reg reg;
  int j;

  reg = quantum_new_qureg_sparse(N+1, N);

  /* Transverse field part */

  for(j=0; j<N; j++)
    {
      reg.state[j] = i^(1 << j);
      reg.amplitude[j] = g;
    }

  reg.state[N] = i;

  /* Interaction part */

  reg.amplitude[N] = V[i];

  return reg;
}

quantum_reg H2(MAX_UNSIGNED i, double t)
{
  return hreg[i];
}

int main()
{
  quantum_reg reg;
  int i, j, k;
  double E0, m, m2;

  printf("# Ground state properties of the transverse Ising chain\n");
  printf("# g: Transverse field in units of the Ising interaction\n");
  printf("# N: Number of spins\n");
  printf("# E_0: Ground state energy\n");
  printf("# m: Spontaneous magnetization\n");
  printf("# x: Spin susceptibility\n");
  printf("# g\t\tN\tE_0\t\tm\t\tx\n");

  for(N=8; N<=18; N+=2)
    {

      /* Precompute interaction energies */

      V = calloc(1<<N, sizeof(int));

      assert(V);

      for(i=0; i<(1<<N); i++)
	{
	  k = 0;
	  for(j=0; j<N-1; j++)
	    {
	      if(i & (1<<j))
		{
		  if(i & (1<<(j+1)))
		    k--;
		  else
		    k++;
		}
	      else
		{
		  if(i & (1<<(j+1)))
		    k++;
		  else
		    k--;
		}
	    }

	  /* Periodic boundary conditions */

	  if(i & (1<<(N-1)))
	    {
	      if(i & 1)
		k--;
		  else
		    k++;
	    }
	    else
	      {
		if(i & 1)
		  k++;
		else
		  k--;
	      }
	    
	  V[i] = k;
	}

      for(g=0.9; g<1.1; g+=0.01)
	{

	  reg = quantum_new_qureg_size(1<<N, N);

	  for(i=0; i<(1<<N); i++)
	    reg.amplitude[i] = rand();

	  hreg = calloc(1<<N, sizeof(quantum_reg));

	  assert(hreg);

	  for(i=0; i<(1<<N); i++)
	      hreg[i] = H(i, 0);

	  E0 = quantum_groundstate(&reg, 1e-12, H2, QUANTUM_SOLVER_LANCZOS, 0);

	  m = 0;
	  m2 = 0;

	  for(i=0; i<(1<<N); i++)
	    {
	      k = 0;
	      for(j=0; j<N; j++)
		{
		  if(i & (1<<j))
		    k--;
		  else
		    k++;
		}
	      m += quantum_prob(reg.amplitude[i])*abs(k);
	      m2 += quantum_prob(reg.amplitude[i])*k*k;
	    }

	  m /= N;
	  m2 /= N;

	  printf("%f\t%i\t%f\t%f\t%f\n", g, N, E0, m, m2-m*m);

	  quantum_delete_qureg(&reg);

	  for(i=0; i<(1<<N); i++)
	    quantum_delete_qureg(&hreg[i]);

	  free(hreg);
	}

      free(V);
    
    }

  return 0;

}