Computing the SYK Spectrum

The Sachdev-Ye-Kitaev (SYK) model is a quantum-mechanical model of disordered fermions with applications in both condensed matter and high-energy physics. This code computes the spectrum of the SYK Hamiltonian with 4-fermion interactions.

Includes a GPU-based implementation of the Lanczos for computing the edge of the spectrum. This is highly optimized and allows going up to at least 46 Majorana fermions. Also includes CPU-based full diagonalization.

Available Programs

These are the main programs (see below for build instructions):

• syk-gpu-lanczos: A GPU (CUDA) based implementation of Lanczos partial diagonalization for Majorana fermions.
  • Run syk-gpu-lanczos --help for a full list of options.
  • Iteratively computes eigenvalues with error estimates starting with the largest ones in absolute value.
  • Supports multi-GPU (uses all available GPUs by default). This is useful when only a single Hamiltonian fits in host memory, but multiple GPUs are available.
• kitaev: A CPU-based full diagonalization of the SYK Hamiltonian.
  • Run kitaev --help to see full list of options.
  • Supports both the Dirac fermion and Majorana fermion vesion.
  • Can compute the full eigenvalue spectrum
  • Can compute thermal fermion 2-point functions (using the eigenvectors)

Other programs and scripts are available for:

• Submitting SLURM jobs (see scripts/submits-xxx)
• Analyzing the data (e.g. computing partition functions)

Building and Unit Testing

Once all dependencies are in installed, simply run make.

Dependencies:

• googletest
• CUDA
• Eigen
• Boost
• LAPACK and BLAS
• gfortran

The locations of these libraries will probably have to be adjusted in Makefile.

Unit tests, separated by required hardware:

• test-kitaev: Test the CPU-based full diagonalization
• test-gpu: Test the GPU-based Lanczos diagonalization
• test-multi-gpu: Test the multi-GPU version of Lanczos