An Attempt to Calculate Energy Eigenvalues in Quantum Systems of Large Sizes

TL;DR

This paper introduces a new method for calculating energy eigenvalues in large quantum systems by effectively truncating the Hamiltonian, requiring less memory than traditional methods like Lanczos, and demonstrating success in various one-dimensional quantum models.

Contribution

The paper presents a novel approach for eigenvalue calculation that reduces memory usage compared to Lanczos, enabling analysis of larger quantum systems with reasonable accuracy.

Findings

Successfully applied to 48-site frustrated spins

Effective for 32-site bosons on a chain

Works for 28-site fermions on a ladder

Abstract

We report an attempt to calculate energy eigenvalues of large quantum systems by the diagonalization of an effectively truncated Hamiltonian matrix. For this purpose we employ a specific way to systematically make a set of orthogonal states from a trial wavefunction and the Hamiltonian. In comparison with the Lanczos method, which is quite powerful if the size of the system is within the memory capacity of computers, our method requires much less memory resources at the cost of the extreme accuracy. In this paper we demonstrate that our method works well in the systems of one-dimensional frustrated spins up to 48 sites, of bosons on a chain up to 32 sites and of fermions on a ladder up to 28 sites. We will see this method enables us to study eigenvalues of these quantum systems within reasonable accuracy.