Fluctuation-exchange supplemented quantum Monte Carlo approach to the Hubbard model

Hague, J. P; Jarrell, Mark and Schulthess, T. C. (2004). Fluctuation-exchange supplemented quantum Monte Carlo approach to the Hubbard model. Physical Review B, 69(16) p. 165113.

DOI: https://doi.org/10.1103/PhysRevB.69.165113

Abstract

This paper introduces an ansatz-based technique for solution of the Hubbard model over two length scales. Short-range correlations are treated exactly using a dynamical cluster approximation quantum Monte Carlo (QMC) simulation, while longer-length-scale physics requiring larger cluster sizes is incorporated through the introduction of the fluctuation-exchange approximation. The properties of the resulting hybrid scheme are examined and the description of local-moment formation is compared to exact results in one dimension (1D). The effects of electron-electron coupling and electron doping on the shape of the Fermi surface are demonstrated in 2D. Causality is examined in both 1D and 2D. We find that the scheme is successful if QMC clusters of N_C>~4 are used (with sufficiently high temperatures in 1D), however, very small QMC clusters of N_C=1 lead to acausal results.

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