NLC

A Numerical Linked Cluster Expansion program for the transverse field Ising model in one and two dimensions.

Developed by Roger Melko, Ann Kallin, and Katie Hyatt.

This project aims to provide a free implementation of the Numerical Linked Cluster Expansion technique developed by Rajiv Singh, Tyler Bryant, and Marcos Rigol. It is written in C++. The application has two possible run-modes: CPU only, and CPU-GPU. In the second, large clusters are handled using a GPGPU code written in CUDA. The CPU version can be run on a single machine or in an MPI configuration.

Installation

You will need to install a few libraries to run the NLC code. If you would like to use the GPU features, you should install the CUDA toolkit, following the instructions provided by NVIDIA for your operating system and architecture. Note that under Linux, if you are running a graphical environment using X11, you may need to temporarily stop X11 in order to install CUDA. NLC uses OpenMP, which is supported in g++ since version 4.2 as well as icpc since 10.1. The Makefiles assume g++. If you are using icpc, simply change g++ after CC to icpc and switch -fopenmp to -openmp on the CFLAGS line. NLC doesn't use any OpenMP 3.0 features.

Running NLC

NLC takes several arguments from param.dat, including whether you would like to find the groundstate of the Hamiltonian (not necessary if you only care about energies), the Sz spin sector you are interested in (not relevant for the TF Ising model, as it is not Sz preserving), and the value of J, the coupling constant for the bond operators. NLC iterates over several values of h, the magnetic field strength. You can easily modify these in NLC_*_TFIM.*. NLC reads in the clusters it will operate on, which are generated by the Graphs. You can specify the file which contains these clusters from the command line when you launch the program, as shown below. If you would like to turn GPU usage on, simply pass -g or --gpu as a command line argument to your executable. GPU selection should be available in a future release. NLC will dump the final energies it calculates into a file whose name you can specify in NLC_*_TFIM.* or as a command line argument using -o $FILENAME or --output $FILENAME$. You will need to select the file containing the graphs NLC will use through the command line, by passing -i $FILENAME or --input $FILENAME. You can also choose at launch whether you would like to calculate magnetization or other properties. If you want to use/create your own clusters, you can use the Graphs utility. Presently this only supports graphs on a square lattice, but further releases should extend this capability.

Usage Examples

Reading in graphs from a file called rectanglegraphs.dat, without calculating magnetization and using the default output file: ./2d-cpu.out -i rectanglegraphs.dat

Reading in graphs from a file called rectanglegraphs.dat, without calculating magnetization and using a custom output file: ./2d-cpu.out -i rectanglegraphs.dat -o rectangleresults.dat

Reading in graphs from a file called order4bondbasedgraphs.dat, calculating magnetization and using the default output file: ./2d-cpu.out -m -i order4bondbasedgraphs.dat

We can also use the GPU executable if we have CUDA installed, as shown below.

Reading in graphs from a file called rectanglegraphs.dat, without calculating magnetization and using the default output file with the GPU: ./2d-gpu.out -g -i rectanglegraphs.dat

Reading in graphs from a file called rectanglegraphs.dat, calculating magnetization and using a custom output file with the GPU: ./2d-gpu.out -g -m -i rectanglegraphs.dat -o gpumagnetization.dat