Practical algorithm for simulating thermal pure quantum states

TL;DR

This paper introduces an efficient algorithm for simulating thermal pure quantum states, enabling faster and more stable computation of thermodynamic properties in quantum many-body systems, thus improving benchmarking capabilities.

Contribution

The authors present a novel algorithm for thermal pure quantum states that is faster and more stable, extending temperature range and reducing computational resources needed.

Findings

Approximately 1000 times faster than previous methods for a 4x4 Hubbard model

Extended accessible temperature range down to β=32

Achieved high performance and numerical stability in implementation

Abstract

The development of novel quantum many-body computational algorithms relies on robust benchmarking. However, generating such benchmarks is often hindered by the massive computational resources required for exact diagonalization or quantum Monte Carlo simulations, particularly at finite temperatures. In this work, we propose a new algorithm for obtaining thermal pure quantum states, which allows efficient computation of both mechanical and thermodynamic properties at finite temperatures. We implement this algorithm in our open-source C++ template library, Physica. Combining the improved algorithm with state-of-the-art software engineering, our implementation achieves high performance and numerical stability. As an example, we demonstrate that for the $4 \times 4$ Hubbard model, our method runs approximately $10^3$ times faster than $\mathcal{H}\Phi$ 3.5.2. Moreover, the accessible temperature range is extended down to $\beta = 32$ across arbitrary doping levels. These advances significantly push forward the frontiers of benchmarking for quantum many-body systems.