Tools /
MpIBcCorrelationCalculate the twopoint correlation function from an IBC timeevolution simulation. Synopsis
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Show the results in Cartesian coordinates.
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Show the argument in radians.
Use complex conjugation to calculate the correlation function up to {$t = 2T$}.
(2D cylinders) Calculate the {$y$} dependence of the correlation function using this string operator representation of the cylinder rotation operator.
Prefix for the input wavefunction filenames, which are of the form [prefix].t[t] (required).
The timestep (required).
Force the input filenames to have this many decimal places.
The number of timesteps to calculate.
The minimum value of x to calculate (default 0).
The maximum value of x to calculate (default 0).
(2D cylinders) The maximum value of y to calculate (requires string ).
The unit cell size to use to determine how many sites to shift for each x step (defaults to the left boundary unit cell size).
The error tolerance for transfer matrix eigenvalues near unity (default 1e12 ).
Subtract this value from the phase (in degrees, or radians if radians is specfied).
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DescriptionThis tool calculates twopoint correlation functions for the form {$$C(x,t) = \langle \Psi_0  O_x(t) O_0(0)^\dagger  \Psi_0 \rangle.$$} If we calculate a timeevolution simulation {$ \Psi(t) \rangle = \mathrm{e}^{\mathrm{i}Ht} O_0^\dagger  \Psi_0 \rangle$}, we can calculate this twopoint correlation function by {$$C(x,t) = \langle \Psi(0)  T^x  \Psi(t) \rangle,$$} where {$T^x$} is the translation operator by {$x$} sites. Furthermore, we can rearrange this to obtain {$$C(x,t) = \langle \Psi(t/2)  T^x  \Psi(t/2) \rangle,$$} and if the initial state is timereversal symmetric, we can obtain {$\Psi(t/2)\rangle$} from the complex conjugate of {$\Psi(t/2)\rangle$}. Hence, using this technique, we can calculate the correlation function up to {$t = 2T$} from a time evolution simulation that only goes to {$t = T$}. Notes
