Computation of ground-state properties of strongly correlated many-body systems by a two-subsystem ground-state approximation

TL;DR

This paper introduces a novel method inspired by multilevel sub-structuring to efficiently compute low-lying eigenvalues of strongly correlated many-body systems by partitioning the state space, significantly reducing computational complexity.

Contribution

The paper develops a new two-subsystem ground-state approximation method based on state space partitioning for strongly correlated systems, inspired by AMLS, and demonstrates its effectiveness on the Hubbard model.

Findings

Method reduces complexity from exponential to manageable size.

Benchmark results show accurate eigenvalues for the Hubbard model.

Approach leverages tensorial structure of Hamiltonians.

Abstract

We present a new approach to compute low lying eigenvalues and corresponding eigenvectors for strongly correlated many-body systems. The method was inspired by the so-called Automated Multilevel Sub-structuring Method (AMLS). Originally, it relies on subdividing the physical space into several regions. In these sub-systems the eigenproblem is solved, and the regions are combined in an adequate way. We developed a method to partition the state space of a many-particle system in order to apply similar operations on the partitions. The tensorial structure of the Hamiltonian of many-body systems make them even more suitable for this approach. The method allows to break down the complexity of large many-body systems to the complexity of two spatial sub-systems having half the geometric size. Considering the exponential size of the Hilbert space with respect to the geometric size this represents a huge advantage. In this work, we present some benchmark computations for the method applied to the one-band Hubbard model.