Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics

TL;DR

This paper introduces a flexible cluster algorithm for quantum impurity problems, enabling precise studies of mesoscopic Kondo physics and potentially benefiting dynamical mean field theory applications.

Contribution

The authors develop a novel cluster algorithm based on spin-chain mapping that efficiently solves quantum impurity models like Anderson and Kondo Hamiltonians.

Findings

Treats mesoscopic fluctuations exactly

Handles large bandwidth-to-temperature ratios easily

Applicable to a wide range of quantum impurity problems

Abstract

Nanoscale physics and dynamical mean field theory have both generated increased interest in complex quantum impurity problems and so have focused attention on the need for flexible quantum impurity solvers. Here we demonstrate that the mapping of single quantum impurity problems onto spin-chains can be exploited to yield a powerful and extremely flexible impurity solver. We implement this cluster algorithm explicitly for the Anderson and Kondo Hamiltonians, and illustrate its use in the ``mesoscopic Kondo problem''. To study universal Kondo physics, a large ratio between the effective bandwidth $D_\mathrm{eff}$ and the temperature $T$ is required; our cluster algorithm treats the mesoscopic fluctuations exactly while being able to approach the large $D_\mathrm{eff}/T$ limit with ease. We emphasize that the flexibility of our method allows it to tackle a wide variety of quantum impurity problems; thus, it may also be relevant to the dynamical mean field theory of lattice problems.