# Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions

## TL;DR

This paper introduces a combined approach using numerical linked cluster expansions and dynamical quantum typicality to efficiently compute time-dependent correlations in quantum many-body systems, achieving faster convergence and scalability.

## Contribution

The novel integration of DQT with NLCE extends the accessible cluster sizes and improves convergence in calculating quantum dynamics, especially in higher dimensions.

## Key findings

- NLCE converges quickly for short to intermediate times
- Combining DQT with NLCE extends cluster size range
- Method is competitive with existing techniques

## Abstract

We demonstrate that numerical linked cluster expansions (NLCE) yield a powerful approach to calculate time-dependent correlation functions for quantum many-body systems in one dimension. As a paradigmatic example, we study the dynamics of the spin current in the spin-1/2 XXZ chain for different values of anisotropy, as well as in the presence of an integrability-breaking next-nearest neighbor interaction. For short to intermediate time scales, we unveil that NLCE yields a convergence towards the thermodynamic limit already for small cluster sizes, which is much faster than in direct calculations of the autocorrelation function for systems with open or periodic boundary conditions. Most importantly, we show that the range of accessible cluster sizes in NLCE can be extended by evaluating the contributions of larger clusters by means of a pure-state approach based on the concept of dynamical quantum typicality (DQT). Even for moderate computational effort, this combination of DQT and NLCE provides a competitive alternative to existing state-of-the-art techniques, which may be applied in higher dimensions as well.