Efficient perturbation theory for quantum lattice models

Abstract

We present a novel approach to long-range correlations beyond dynamical mean-field theory through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Neel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte-Carlo (QMC) results. An illustration of how the approach captures and allows to distinguish short- and long-range correlations is given.

5 pages, 5 figures; revised version with emphasis on the ladder approximation

References in corpus (10)

• Fermi-liquid instabilities at magnetic quantum phase transitions
• Dynamical vertex approximation - a step beyond dynamical mean field theory
• Variational cluster approach to correlated electron systems in low dimensions
• Cluster Dynamical Mean Field Theory of the Mott Transition
• Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs
• Pseudogaps in Strongly Correlated Metals: A generalized dynamical mean-field theory approach
• Influence of Spatial Correlations in Strongly Correlated Electron Systems: Extension to Dynamical Mean Field Approximation
• Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions
• Cluster Dual Fermion Approach to Nonlocal Correlations
• Lattice susceptibility for 2D Hubbard Model within dual fermion method

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