Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics

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.

4 pages, 3 figures

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Cited by in corpus (12)

• Many-Body Physics and Quantum Chaos
• Spectroscopy of the Kondo Problem in a Box
• Nonperturbative Scaling Theory of Free Magnetic Moment Phases in Disordered Metals
• Transport through side-coupled double quantum dots: from weak to strong interdot coupling
• On the Sign Problem in the Hirsch-Fye Algorithm for Impurity Problems
• Quantum Phase Transition and Dynamically Enhanced Symmetry in Quadruple Quantum Dot System
• Transport through side-coupled multilevel double quantum dots in the Kondo regime
• Ground State and Excitations of Quantum Dots with "Magnetic Impurities"
• Mesoscopic Anderson Box: Connecting Weak to Strong Coupling
• From Weak- to Strong-Coupling Mesoscopic Fermi Liquids
• Conductance of Quantum Impurity Models from Quantum Monte Carlo
• Fermi-liquid regime of the mesoscopic Kondo problem