Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model

TL;DR

This paper introduces a simple, efficient quantum typicality method to study transport in the Holstein model, providing accurate frequency-dependent mobilities and insights into vertex corrections, with potential for broader applications.

Contribution

The paper presents a numerically exact QT approach for transport properties, demonstrating its accuracy and efficiency in the Holstein model and its potential for wider use.

Findings

QT accurately computes frequency-dependent mobilities

Method compares favorably with other exact techniques

Analysis of vertex corrections in transport properties

Abstract

We investigate the transport properties of the Holstein model using the numerically exact quantum typicality (QT) approach. Roughly speaking, QT exploits the fact that even a single, randomly chosen pure state can effectively represent the full statistical ensemble in a high-dimensional Hilbert space. This allows us to compute frequency-dependent mobilities, representative of the thermodynamic limit, that are well-converged with respect to all numerical parameters. Our results are compared against other numerically exact methods, and used to analyze the contribution of vertex corrections to frequency-dependent mobility. The promising accuracy and efficiency of the QT approach suggest its applicability to a broader class of Hamiltonians.