ALPS Custom Measurement

Defining your custom measurements

If the default measurements performed by your ALPS application do not cover what you need, you can define custom measurements directly in the parameter file. The general syntax is as follows:

MEASURE_LOCAL[Name]=Op
MEASURE_AVERAGE[Name]=Op

Here Name is the name under which the measurement appears in the XML output, and Op is a site or bond operator, which must already be defined for the model — either a built-in operator from the model library or one you defined yourself (see Quantum Operators). MEASURE_AVERAGE measures the quantum-mechanical, and (for finite-temperature simulations) thermodynamic, expectation value of Op. MEASURE_LOCAL measures the expectation value of Op at each site of the lattice; Op must therefore be local, i.e. it can only have site terms, not bond terms.

MEASURE_CORRELATIONS[Name]="Op1:Op2"
MEASURE_CORRELATIONS[Name]=Op

MEASURE_CORRELATIONS measures the correlations of the operators Op1 and Op2 for all inequivalent pairs of sites of the lattice. The second form above, MEASURE_CORRELATIONS[Name]=Op, is equivalent to MEASURE_CORRELATIONS[Name]="Op:Op". At present, only two-site correlation functions can be computed, so both Op1 and Op2 must be site operators.

MEASURE_STRUCTURE_FACTOR[Name]=Op

This measures the structure factor for the operator Op, i.e. the lattice Fourier transform of the corresponding correlation function, evaluated at the momentum eigenstates of the simulation lattice.

Which ALPS applications support this

The MEASURE_LOCAL/MEASURE_AVERAGE/MEASURE_CORRELATIONS/MEASURE_STRUCTURE_FACTOR syntax above is not interpreted by the model or lattice XML machinery itself — it is optional functionality that each simulation code has to wire in separately, and in practice only a subset of ALPS applications do:

For the codes marked “full support” above (loop, worm, sse/sse2/sse4, dwa, fulldiag, dmrg), a custom Name that collides with one of the code’s built-in observable names (e.g. Local Density, Spin Correlations) is silently skipped in favor of the built-in one, with a note to standard error — so give your custom measurements distinctive names.

The matrix-product-state DMRG code (mps_optim/mps_meas) does not use the mechanism described on this page at all; it has its own reimplementation that accepts MEASURE_LOCAL, MEASURE_AVERAGE, and MEASURE_CORRELATIONS with the same meaning as above, plus several extensions with no equivalent elsewhere in ALPS: MEASURE_HALF_CORRELATIONS (like MEASURE_CORRELATIONS, but without exchanging the order of operators), MEASURE_LOCAL_AT (apply a sequence of operators to an explicit, arbitrary tuple of sites), and boolean flags such as MEASURE[EnergyVariance], MEASURE[Entropy], and MEASURE[Renyi2].

Since support varies so much from code to code, always check the parameter reference or tutorial for the specific application you are using before relying on any of these statements.

Further tricks and workarounds

Measuring off-diagonal quantities in QMC codes is in general non-trivial and is hard to implement in a generic fashion. If your favorite QMC program refuses to perform your favorite measurement, you may need to modify the source code.

In certain cases, however, several tricks can be used. One useful trick is to enlarge the site basis of your model. Consider the following example: using the worm code to simulate the Bose-Hubbard model on an inhomogeneous lattice, we want to measure the second moment of the local density distribution $\langle n_i^2\rangle$. Since the worm code does not work in the site basis, it will not perform measurements for such an operator directly. One possible solution is to patch the boson site basis used by the Bose-Hubbard Hamiltonian, adding an n2 operator for the squared density:

<SITEBASIS name="boson">
<PARAMETER name="Nmax" default="infinity"/>
<QUANTUMNUMBER name="N" min="0" max="Nmax"/>
<OPERATOR name="bdag" matrixelement="sqrt(N+1)">
    <CHANGE quantumnumber="N" change="1"/>
</OPERATOR>
<OPERATOR name="b" matrixelement="sqrt(N)">
    <CHANGE quantumnumber="N" change="-1"/>
</OPERATOR>
<OPERATOR name="n" matrixelement="N"/>
<OPERATOR name="n2" matrixelement="N*N"/>   <!-- added -->
</SITEBASIS>

With this patch, one can define the corresponding measurements in the usual fashion, e.g.

MEASURE_LOCAL[Local density squared]="n2"
MEASURE_CORRELATIONS[Density squared, correlations]="n2:n2"

For how the operators used above are defined, see Quantum Operators. For an overview of model definitions in general, see ALPS Model Definitions. For the other ALPS documentation sections, see the General Introduction.