Worm Algorithm
Introduction
The worm code provides a full generic implementation for Quantum Monte Carlo (QMC) simulations based on the worm algorithms which was invented by N. Prokof’ev and collaborators. Technically, it provides a continuous-time QMC code based on a path integral representation of the partition function.
The current implementation allows to simulate the following models on arbitrary lattices:
- Quantum spin (unfrustrated) models with arbitrary spin size, magnetic field and anisotropy
- (Softcore) bosonic models without a sign problem
Support for simulations with a sign problem could be added if desired.
Running a simulation
An example simulation is discussed in the tutorial.
Input parameters
The worm code uses the common input parameters discussed here.
Parameters for experts
In addition, specific simulations parameters can be assigned (use only if you see what it means!):
| Parameter | Default | Meaning |
|---|---|---|
| SKIP | 1 | the number of Monte Carlo sweeps between each measurement |
| RESTRICT_MEASUREMENTS[N] | if defined this restricts measurements to configurations where the quantum number N (particle number) has the value given as this parameter. Note that the simulation will still be performed in the grand canonical ensemble and the chemical potential needs to be tuned to the right range, to actually sample configurations with the desired particle number. | |
| RESTRICT_MEASUREMENTS[Sz] | if defined this restricts measurements to configurations where the quantum number Sz (magnetization) has the value given as this parameter. Note that the simulation will still be performed in the grand canonical ensemble and the magnetic field needs to be tuned to the right range, to actually sample configurations with the desiredmagnetization. | |
| WORMS_PER_KINK | 1 | determines how often a worm should visit a kink on average per sweep. |
| MEASURE_GREEN | false | flag that indicates whether the Green’s function should be measured. Don’t use - this is untested! |
Compile time parameters
Furthermore, at compile time you can define the following variables in the file WRun.h
| Parameter | Meaning |
|---|---|
| NONLOCAL | undefine to speed up the code for local interactions. |
| USE_VECTOR | define to use a std::vector instead of a std::list as data structure. |
| USE_SET | define to use a std::set instead of a std::list as data structure. |
Measurements
The following observables are measured by the worm code application:
| Name | Description |
|---|---|
| Energy | total energy of the system |
| Energy Density | energy per site |
| Density | particle number (for bosonic models) |
| Density^2 | square of the particle number (for bosonic models) |
| Stiffness | stiffness of the system (for bosonic models) |
| Green’s function | Green’s function (works only for local interactions) |
Contributors
The following persons have contributed to the worm application:
- Simon Trebst
- Matthias Troyer