Comparison of two-quantum-cluster approximations

Th A. Maier; M. Jarrell

Comparison of two-quantum-cluster approximations

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21 Scopus citations

Abstract

We provide microscopic diagrammatic derivations of the molecular coherent potential approximation (MCA) and dynamical cluster approximation (DCA) and show that both are Φ derivable. The MCA (DCA) maps the lattice onto a self-consistently embedded cluster with open (periodic) boundary conditions, and therefore violates (preserves) the translational symmetry of the original lattice. As a consequence of the boundary conditions, the MCA (DCA) converges slowly (quickly) with corrections O(1/L_c) [O(1/L_c²)], where L_c is the linear size of the cluster. These analytical results are demonstrated numerically for the onedimensional symmetric Falicov-Kimball model.

Original language	English
Article number	041104
Pages (from-to)	411041-411044
Number of pages	4
Journal	Physical Review B - Condensed Matter and Materials Physics
Volume	65
Issue number	4
State	Published - Jan 15 2002
Externally published	Yes

Cite this

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abstract = "We provide microscopic diagrammatic derivations of the molecular coherent potential approximation (MCA) and dynamical cluster approximation (DCA) and show that both are Φ derivable. The MCA (DCA) maps the lattice onto a self-consistently embedded cluster with open (periodic) boundary conditions, and therefore violates (preserves) the translational symmetry of the original lattice. As a consequence of the boundary conditions, the MCA (DCA) converges slowly (quickly) with corrections O(1/Lc) [O(1/Lc2)], where Lc is the linear size of the cluster. These analytical results are demonstrated numerically for the onedimensional symmetric Falicov-Kimball model.",

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AB - We provide microscopic diagrammatic derivations of the molecular coherent potential approximation (MCA) and dynamical cluster approximation (DCA) and show that both are Φ derivable. The MCA (DCA) maps the lattice onto a self-consistently embedded cluster with open (periodic) boundary conditions, and therefore violates (preserves) the translational symmetry of the original lattice. As a consequence of the boundary conditions, the MCA (DCA) converges slowly (quickly) with corrections O(1/Lc) [O(1/Lc2)], where Lc is the linear size of the cluster. These analytical results are demonstrated numerically for the onedimensional symmetric Falicov-Kimball model.

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JF - Physical Review B - Condensed Matter and Materials Physics

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Comparison of two-quantum-cluster approximations

Abstract

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