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scrambling
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Calculate mutual information in all regions.

This commit is contained in:
Andrius Štikonas 2015-04-25 16:39:38 +01:00
parent ddf89b6f80
commit a56e5420ca
1 changed files with 46 additions and 34 deletions
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scrambling.cpp
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@ -31,13 +31,16 @@ int main()
double tPlus = 0; // time on the left boundary
double tMinus = 0; // time on the right boundary
alpha = 0.4; // encodes the conformal dimention of local operator h_Psi
double y = 1; // endpoint of interval A
double L = 5; // length of interval A
double y = 3; // endpoint of interval A
double L = 15; // length of interval A
double epsilon = 0.01; // smearing parameter
beta = 10; // inverse temperature
double tOmega = 5.4418; // thermal state is perturbed by operator inserted at time -tOmega
// double tOmega = /*5.4418*/; // thermal state is perturbed by operator inserted at time -tOmega
double c = 600; // central charge. Must be large in our approximation
// End of parameters
for(unsigned int i = 0; i < 1000; ++i)
{
double tOmega = i*2*L/1000;
// Operator insertion points: Left boundary
std::complex<double> x1 (0, -epsilon), x4 (0, epsilon), x1bar, x4bar;
@ -69,12 +72,21 @@ int main()
std::complex<double> z5bar = crossRatio(x1bar, x5bar, x3bar, x4bar);
// Now we calculate entanglement entropies using Fitzpatrick, Kaplan, Walters formula.
double S_A = c/6 * log(Fitzpatrick(zA, zAbar, 2*M_PI));
double S_A = c/6 * log(Fitzpatrick(zA, zAbar, y < tMinus + tOmega && tMinus + tOmega < y + L ? 2*M_PI : 0));
// std::cerr << "S_A = " << S_A << std::endl;
// double S_A_analytic = c/6 * log(beta/M_PI/epsilon/sinh(M_PI*L/beta)*sinh(M_PI/beta*(y+L-tMinus-tOmega))*sinh(M_PI/beta*(tMinus+tOmega-y)) * sin(M_PI*alpha)/alpha);
// double S_A_analytic = 0;
// std::cerr << "S_A (analytic) = " << S_A_analytic << std::endl;
double S_B = c/6 * log(Fitzpatrick(zB, zBbar, 0));
double S_union = c/6 * log(Fitzpatrick(z2, z2bar, 2*M_PI) * Fitzpatrick(z5, z5bar, 0));
double S_union = c/6 * log(Fitzpatrick(z2, z2bar, y < tMinus + tOmega ? 2*M_PI : 0) * Fitzpatrick(z5, z5bar, y +L < tMinus + tOmega ? -2*M_PI : 0));
// std::cerr << "S_A+B = " << S_union << std::endl;
double S_union_analytic = c/3 * log(beta/M_PI/epsilon * sin(M_PI*alpha)/alpha) + c/6* log(sinh(M_PI/beta*(tMinus + tOmega - y)) * cosh(M_PI/beta*(tPlus + tOmega - y)) * sinh(M_PI/beta*(tMinus + tOmega - y - L)) * cosh(M_PI/beta*(tPlus + tOmega - y - L)));
// std::cerr << "S_A+B (analytic) = " << S_union_analytic << std::endl;
double S_thermal = 2*c/3 * log(sinh(M_PI*L/beta)/cosh(M_PI/beta*(tMinus-tPlus)));
double I = S_A + S_B - S_union + S_thermal;
std::cout << I << std::endl;
// double I_analytic = S_A_analytic - S_union_analytic + S_thermal;
std::cout << tOmega << "\t" << I /*<< "\t" << I_analytic*/ << std::endl;
}
return 0;
}