Computing excited eigenstates using inexact Lanczos methods and tree tensor network states

TL;DR

This paper introduces a novel method combining inexact Lanczos algorithms with tree tensor network states to efficiently compute excited eigenstates in complex quantum many-body systems, demonstrated on vibrational states of molecules.

Contribution

It develops a new approach integrating inexact Lanczos with TTNSs for accurate excited state calculations, applicable to various quantum systems.

Findings

Successfully computed 122 excited states in acetonitrile

Determined Fermi resonance states of Zundel ion

Obtained excited states of Eigen ion with high accuracy

Abstract

To understand the dynamics of quantum many-body systems, it is essential to study excited eigenstates. While tensor network states have become a standard tool for computing ground states in computational many-body physics, obtaining accurate excited eigenstates remains a significant challenge. In this work, we develop an approach that combines the inexact Lanczos method, which is designed for efficient computations of excited states, with tree tensor network states (TTNSs). We demonstrate our approach by computing excited vibrational states for three challenging problems: (1) 122 states in two different energy intervals of acetonitrile (12-dimensional), (2) Fermi resonance states of the fluxional Zundel ion (15-dimensional), and (3) selected excited states of the fluxional and very correlated Eigen ion (33-dimensional). The proposed TTNS inexact Lanczos method is directly applicable to other quantum many-body systems.