const iTEBD<Tensor>
evolve_itime(iTEBD<Tensor> psi, const Tensor &H12,
double dt, tensor::index nsteps,
double tolerance, tensor::index max_dim,
tensor::index deltan)
{
static const double FR_param[5] =
{0.67560359597983, 1.35120719195966, -0.17560359597983, -1.70241438391932};
Tensor eH12[4];
int method = 2;
switch (method) {
case 1:
/* Second order Trotter expansion */
eH12[1] = linalg::expm((-dt/2) * H12);
case 0:
/* First order Trotter expansion */
eH12[0] = linalg::expm((-dt) * H12);
break;
default:
/* Fourth order Trotter expansion */
for (int i = 0; i < 4; i++) {
eH12[i] = linalg::expm((-dt*FR_param[i]) * H12);
}
}
Tensor Id = Tensor::eye(H12.rows());
double time = 0;
double E = energy(psi, H12), S = psi.entropy();
std::cout.precision(5);
std::cout << nsteps << ", " << dt << " x " << deltan << " = " << dt * deltan << std::endl;
RTensor S_growth((deltan < 10)? 10 : deltan);
RTensor E_growth((deltan < 10)? 10 : deltan);
S_growth.fill_with_zeros();
E_growth.fill_with_zeros();
bool stop = false;
for (size_t i = 0; (i < nsteps) && (!stop); i++) {
switch (method) {
case 0:
psi = psi.apply_operator(eH12[0], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[0], 1, tolerance, max_dim);
break;
case 1:
psi = psi.apply_operator(eH12[1], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[0], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[1], 0, tolerance, max_dim);
break;
default:
psi = psi.apply_operator(eH12[0], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[1], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[2], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[3], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[2], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[1], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[0], 0, tolerance, max_dim);
}
double newE = energy(psi, H12);
double newS = psi.entropy();
double dS = S - newS;
double dE = E - newE;
double dSdt = avg_change(i, S_growth, dS) / dt;
double dEdt = avg_change(i, E_growth, dE) / dt;
S = newS;
E = newE;
time += dt;
if (i > E_growth.size() && ((abs(dSdt) < 1e-6) && (dEdt <= 1e-6))) {
std::cout << "Entropy and energy converged" << std::endl;
stop = true;
}
if ((deltan && (i % deltan == 0)) || stop) {
std::cout << "t=" << time << ";\tE=" << E << ";\tS=" << S
<< ";\tl=" << std::max(psi.left_dimension(0),
psi.right_dimension(0))
<< std::endl;
std::cout << "\tdS=" << dS << ";\tdE=" << dE << std::endl;
std::cout << "\tdSdt=" << dSdt << ";\tdEdt=" << dEdt << std::endl;
}
}
return psi;
}
const iTEBD<Tensor>
evolve_itime(iTEBD<Tensor> psi, const Tensor &H12,
double dt, tensor::index nsteps,
double tolerance, tensor::index max_dim,
tensor::index deltan, int method,
std::vector<double> *energies,
std::vector<double> *entropies)
{
static const double FR_param[5] =
{0.67560359597983, 1.35120719195966, -0.17560359597983, -1.70241438391932};
Tensor eH12[4];
//int method = 2;
switch (method) {
case 1:
/* Second order Trotter expansion */
eH12[1] = linalg::expm((-dt/2) * H12);
case 0:
/* First order Trotter expansion */
eH12[0] = linalg::expm((-dt) * H12);
break;
default:
/* Fourth order Trotter expansion */
for (int i = 0; i < 4; i++) {
eH12[i] = linalg::expm((-dt*FR_param[i]) * H12);
}
}
Tensor Id = Tensor::eye(H12.rows());
double time = 0;
psi = psi.canonical_form();
double E = energy(psi, H12), S = psi.entropy();
if (energies)
energies->push_back(E);
if (entropies)
entropies->push_back(S);
if (!deltan) {
deltan = 1;
}
std::cout.precision(5);
std::cout << nsteps << ", " << dt << " x " << deltan
<< " = " << dt * deltan << std::endl;
std::cout << "t=" << time
<< ";\tE=" << E << "; dE=" << 0.0
<< ";\tS=" << S << "; dS=" << 0.0
<< ";\tl=" << std::max(psi.left_dimension(0),
psi.right_dimension(0))
<< std::endl
<< "l = " << matrix_form(real(psi.left_vector(0)))
<< std::endl;
for (size_t phases = (nsteps + deltan - 1) / deltan; phases; phases--) {
for (size_t i = 0; (i < deltan); i++) {
switch (method) {
case 0:
psi = psi.apply_operator(eH12[0], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[0], 1, tolerance, max_dim);
break;
case 1:
psi = psi.apply_operator(eH12[1], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[0], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[1], 0, tolerance, max_dim);
break;
default:
psi = psi.apply_operator(eH12[0], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[1], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[2], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[3], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[2], 0, tolerance, max_dim);
psi = psi.apply_operator(eH12[1], 1, tolerance, max_dim);
psi = psi.apply_operator(eH12[0], 0, tolerance, max_dim);
}
time += dt;
}
psi = psi.canonical_form();
double newE = energy(psi, H12);
double newS = psi.entropy();
if (energies)
energies->push_back(newE);
if (entropies)
entropies->push_back(newS);
std::cout << "t=" << time
<< ";\tE=" << newE << "; dE=" << newE-E
<< ";\tS=" << newS << "; dS=" << newS-S
<< ";\tl=" << std::max(psi.left_dimension(0),
psi.right_dimension(0))
<< std::endl
<< "l = " << matrix_form(real(psi.left_vector(0)))
<< std::endl;
E = newE;
S = newS;
}
return psi;
}