Divide and conquer the Hilbert space of translation-symmetric spin systems

TL;DR

This paper introduces a divide-and-conquer approach to efficiently implement translation symmetries in finite quantum spin systems, enabling the study of larger Hamiltonian matrices beyond 10^11 dimensions.

Contribution

The authors develop an extended sublattice coding method that allows on-the-fly Hamiltonian matrix generation, significantly increasing the accessible system sizes for iterative quantum spin calculations.

Findings

Enables handling of Hamiltonian matrices over 10^11 in dimension.

Improves computational efficiency in symmetry utilization.

Facilitates studies of larger frustrated quantum spin systems.

Abstract

Iterative methods that operate with the full Hamiltonian matrix in the untrimmed Hilbert space of a finite system continue to be important tools for the study of one- and two-dimensional quantum spin models, in particular in the presence of frustration. To reach sensible system sizes such numerical calculations heavily depend on the use of symmetries. We describe a divide-and-conquer strategy for implementing translation symmetries of finite spin clusters, which efficiently uses and extends the "sublattice coding" of H. Q. Lin. With our method, the Hamiltonian matrix can be generated on-the-fly in each matrix vector multiplication, and problem dimensions beyond 10^11 become accessible.