Improved Hilbert space exploration algorithms for finite temperature calculations

TL;DR

This paper introduces an improved Hilbert space exploration algorithm tailored for finite-temperature correlation calculations in the Lieb-Liniger model, enhancing computational efficiency for high-entropy states.

Contribution

The authors develop a novel Hilbert space exploration algorithm optimized for finite-entropy states, improving correlation function computations at finite temperatures.

Findings

Enhanced efficiency in computing finite-temperature correlations.

Better handling of high-entropy states compared to previous methods.

Potential for broader application in strongly-interacting quantum systems.

Abstract

Computing correlation functions in strongly-interacting quantum systems is one of the most important challenges of modern condensed matter theory, due to their importance in the description of many physical observables. Simultaneously, this challenge is one of the most difficult to address, due to the inapplicability of traditional perturbative methods or the few-body limitations of numerical approaches. For special cases, where the model is integrable, methods based on the Bethe Ansatz have succeeded in computing the spectrum and given us analytical expressions for the matrix elements of physically important operators. However, leveraging these results to compute correlation functions generally requires the numerical evaluation of summations over eigenstates. To perform these summations efficiently, Hilbert space exploration algorithms have been developed which has resulted most notably in the ABACUS library. While this performs quite well for correlations on ground states or low-entropy states, the case of high entropy states (most importantly at finite temperatures or after a quantum quench) is more difficult, and leaves room for improvement. In this work, we develop a new Hilbert space exploration algorithm for the Lieb-Liniger model, specially tailored to optimize the computational order on finite-entropy states for correlations of density-related operators.