SL2Cfoam-next

A high performance code for EPRL spin foam amplitudes

SL2Cfoam-next is a library for computing spin foam amplitudes of covariant Loop Quantum Gravity. The library is optimized for computing the Lorentzian EPRL vertex amplitude [Engle et al., 2008] for all possible boundary intertwiners at fixed boundary spins. The amplitudes are stored in 5-dimensional arrays of double-precision numbers and can be manipulated using the provided C bindings or a convenient Julia module.

Quickstart

To start computing spin foam amplitudes immediately, follow the new quickstart guide.

Features

The computation uses the EPRL splitting introduced in [Speziale, 2017]. In particular, the library splits the amplitude in the computation of: (i) SU(2) recoupling symbols; (ii) SL(2,C) dipole amplitudes (boosters) and (iii) shelled sums. The library exports methods to compute:

• Lorentzian EPRL vertex amplitudes as tensors
• BF vertex amplitudes as tensors
• booster coefficients as tensors
• Livine-Speziale coherent state coefficients as vectors

The Julia interface implements all these methods as well as additional methods for contracting vertex tensors with coherent states and offloading the contractions to the GPU. Two additional tools are provided as standalone programs to compute a single amplitude and to store a full vertex tensor.

Dependencies

The library depends on:

1. GNU GMP, MPFR, MPC
2. quadmath (GCC extension)
3. wigxjpf and fastwigxj [Johansson et al., 2015]
4. OpenMP
5. a BLAS implementation
6. OpenMPI (optional)
7. Julia >= 1.5 (optional)
8. Julia modules: HalfIntegers, CUDA (optional)

Compilation

The library can be compiled by typing make. This compiles the shared library, the test programs and the library tools. There are additional flags that can be provided. For example:

• type make BLAS=mkl/blasfeo/system to choose between different BLAS libraries [Frison et al., 2018] (default is MKL)
• type make DEBUG=1 to build the debug version
• type make MPI=1 to build the MPI version
• type make OMP=0 to disable builtin OpenMP parallelization

The previous flags can be combined. The library searches for folders wigxjpf, fastwigxj and blasfeo (optional) under ext/. The variable MKLROOT must be set for compiling with MKL. The library has been tested with GCC version 8.1 or greater.

You can provide flags for GCC or the linker using the option ADD_CFLAGS=... after make. This can be used for example for providing a different definition of the Y-map. The default definition sets the irrep continuous label to Immirzi * (j+1). Compiling with ADD_CFLAGS=-DRHO_GJ sets the Y-map to Immirzi * j.

Usage (C interface)

See inc/sl2cfoam.h.

Usage (Julia interface)

To use the Julia interface the module SL2Cfoam must be imported. You must init the C library calling SL2Cfoam.cinit(...) providing:

1. a root folder with fastwigxj tables (one file with extension .6j and one with .3j)
2. the Immirzi parameter (can be later changed at runtime)
3. a SL2Cfoam.Config object with additional configuration

When finished call SL2Cfoam.cclear(). To compute a vertex tensor call vertex_compute(...) providing a list of 10 spins, the number of shells (from 0 to 50) and optionally a range of intertwiners. You can load vertex tensors computed with the C library calling vertex_load(...). You can compute coherent states coefficients calling coherentstates_compute(...). You can contract a vertex tensor with 1 to 5 coherent states coefficients using contract(v, cs...). See julia/SL2Cfoam.jl for more functions and details. For GPU offloading you must load the additional modules SL2CfoamGPU and CUDA.

License

SL2CFOAM-NEXT is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

SL2CFOAM-NEXT is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with SL2CFOAM-NEXT. If not, see http://www.gnu.org/licenses/.

If you use the library, cite the following paper: "Francesco Gozzini, A high-performance code for EPRL spin foam amplitudes, Class. Quantum Grav. 38, 225010, doi:10.1088/1361-6382/ac2b0b."