Matrix Product Toolkit | Tools / MpICorrelation

The mp-icorrelation command calculates correlation functions on an iMPS. It does this more efficiently than a sequence of mp-expectation commands.

Synopsis

mp-icorrelation [options] <psi> <operator1> <operator2>

Calculates {$\bigbraket{\psi}{\,\mbox{operator1}(0)\;\mbox{operator2}(x)\,}{\psi}$}

Options

--help

show help message

-c, --cart

Show the results in cartesian coordinates

-p, --polar

show the results in polar coordinates

-r, --real

Show the real part of the result

-i, --imag

show the imaginary part of the result

-m, --mag

Show the magnitude part of the result

-a, --arg

show the argument part of the result

--radians

show the argument in radians

-l, --lattice

As an alternative to specifying the lattice separately for each operator, you can set it once here and it will implicitly use this lattice, as if you used the syntax lattice:operator

-s, --string=X

Evaluate the string correlation function {$\bigbraket{\psi}{\mbox{operator1}(0)\,X(1)\,X(2)\,\cdots \,X(x-1)\,\mbox{operator2}(x)}{\psi}$}. The string operator must be in the form of a product MPO, with a compatible unit cell.

-d, --includefirst

Multiply Operator1 by the string operator {$X(0)$}

-u, --unitcell=N

Used this unit cell size (default is the lattice unit cell size)

-n, --length=N

Length of the correlation to evaluate, default 100 unit cells

--average

Average the wavefunction over shifts of the lattice unit cell. Only meaningful when the wavefunction unit cell is larger than the lattice unit cell.

--connected

Calculate the connected part of the correlation function, {$\bigbraket{\psi}{\,\mbox{operator1}(0)\,\mbox{operator2}(x)\,}{\psi} - \bigbraket{\psi}{\mbox{operator1}(0)}{\psi} \bigbraket{\psi}{\mbox{operator2}(x)}{\psi} $}

Description

This command calculates correlation functions of local operators. Operator1 and Operator2 (and optionally, the --string operator) are local operators and they must be contained within one unit cell (from the lattice, or from the --unitcell option).

Examples

Spin chain correlation function

mp-icorrelation -l lattice psi "Sz(0)" "Sz(0)"

This will calculate 100 sites of the correlation between sites x and y, where x is each site in the wavefunction unit cell (eg, for a spin-1/2 chain if the unit cell is 2 sites, then we get both x=0 and x=1), and y ranging from 0 to 100.
Spin-1/2 chain correlation function

\\For a spin-1/2 chain with a unit cell of 2 sites, we typically want to average over the two sites in the unit cell, and print one number for each distance.
mp-icorrelation -l lattice psi "Sz(0)" "Sz(0)" --average