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/* 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(®, 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(®);
for(i=0; i<(1<<N); i++)
quantum_delete_qureg(&hreg[i]);
free(hreg);
}
free(V);
}
return 0;
}
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