Efficient variational diagonalization of fully many-body localized Hamiltonians

TL;DR

This paper presents a scalable variational method using unitary matrix-product operators to efficiently approximate all eigenstates of fully many-body localized Hamiltonians in one dimension, significantly reducing computational costs.

Contribution

The authors introduce a novel UMPO-based variational approach that scales linearly with system size, enabling efficient approximation of eigenstates in fMBL systems.

Findings

Accurately approximates eigenstates of disordered Heisenberg chains

Scales linearly with system size for fixed bond dimension

Shows good agreement with exact diagonalization results

Abstract

We introduce a unitary matrix-product operator (UMPO) based variational method that approximately finds all the eigenstates of fully many-body localized (fMBL) one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed bond dimension of the UMPO ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.