Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems

TL;DR

This paper introduces a sublattice coding algorithm and a distributed memory parallelization scheme that significantly improve the efficiency of exact diagonalization computations for large quantum many-body systems, enabling analysis of larger systems.

Contribution

The paper presents novel algorithmic and parallelization techniques that enhance memory efficiency and scalability in exact diagonalization of quantum systems with discrete symmetries.

Findings

Able to analyze systems of up to 50 spin-1/2 particles

Achieved faster computations with reduced memory usage

Demonstrated effective parallelization on distributed memory systems

Abstract

We present algorithmic improvements for fast and memory-efficient use of discrete spatial symmetries in Exact Diagonalization computations of quantum many-body systems. These techniques allow us to work flexibly in the reduced basis of symmetry-adapted wave functions. Moreover, a parallelization scheme for the Hamiltonian-vector multiplication in the Lanczos procedure for distributed memory machines avoiding load balancing problems is proposed. We demonstrate that using these methods low-energy properties of systems of up to 50 spin-1/2 particles can be successfully determined.