Probing the Dynamical Structure Factor of Quantum Spin Chains via Low-Temperature Gibbs States with Matrix Product State Subspace Expansion

TL;DR

This paper introduces a novel tensor network method using generating-function matrix product states to accurately simulate low-temperature properties of quantum spin chains, overcoming previous scalability and accuracy challenges.

Contribution

The authors develop a new approach with GFMPS that efficiently generates excited states to approximate Gibbs states at low temperatures, improving upon existing tensor network techniques.

Findings

High accuracy in reproducing exact diagonalization results

Excellent agreement with experimental data

Effective at low-temperature regimes

Abstract

Studying finite-temperature properties with tensor networks is notoriously difficult, especially at low temperatures, due to the rapid growth of entanglement and the complexity of thermal states. Existing methods like purification and minimally entangled typical thermal states offer partial solutions but struggle with scalability and accuracy in low-temperature regime. To overcome these limitations, we propose a new approach based on generating-function matrix product states (GFMPS). By directly computing a large set of Bloch-type excited states, we construct Gibbs states that moderate the area-law constraint, enabling accurate and efficient approximation of low-temperature thermal behavior. Our benchmark results show magnificent agreement with both exact diagonalization and experimental observations, validating the accuracy of our approach. This method offers a promising new direction for overcoming the longstanding challenges of studying low-temperature properties within the tensor network framework. We also expect that our method will facilitate the numerical simulation of quantum materials in comparison with experimental observations.