TY - JOUR
T1 - Dynamical cluster approximation with continuous lattice self-energy
AU - Staar, Peter
AU - Maier, Thomas
AU - Schulthess, Thomas C.
PY - 2013/9/3
Y1 - 2013/9/3
N2 - The dynamical cluster approximation (DCA) is a systematic extension beyond the single-site approximation in dynamical mean field theory, to include spatially nonlocal correlations in quantum many-body simulations of strongly correlated systems. We extend the DCA with a continuous lattice self-energy in order to achieve better convergence with cluster size. This method, which we call DCA+, cures the cluster-shape dependence problems of the DCA, without suffering from causality violations of previous attempts to interpolate the cluster self-energy. A practical approach based on standard inference techniques is given to deduce the continuous lattice self-energy from an interpolated cluster self-energy. We study the pseudogap region of a hole-doped two-dimensional Hubbard model and find that, in the DCA+algorithm, the self-energy and pseudogap temperature T* converge monotonously with cluster size. Introduction of a continuous lattice self-energy eliminates artificial long-range correlations and thus significantly reduces the sign problem of the quantum Monte Carlo cluster solver in the DCA +algorithm compared to the normal DCA. Simulations with much larger cluster sizes thus become feasible, which, along with the improved convergence in cluster size, raises hope that precise extrapolations to the exact infinite cluster size limit can be reached for other physical quantities as well.
AB - The dynamical cluster approximation (DCA) is a systematic extension beyond the single-site approximation in dynamical mean field theory, to include spatially nonlocal correlations in quantum many-body simulations of strongly correlated systems. We extend the DCA with a continuous lattice self-energy in order to achieve better convergence with cluster size. This method, which we call DCA+, cures the cluster-shape dependence problems of the DCA, without suffering from causality violations of previous attempts to interpolate the cluster self-energy. A practical approach based on standard inference techniques is given to deduce the continuous lattice self-energy from an interpolated cluster self-energy. We study the pseudogap region of a hole-doped two-dimensional Hubbard model and find that, in the DCA+algorithm, the self-energy and pseudogap temperature T* converge monotonously with cluster size. Introduction of a continuous lattice self-energy eliminates artificial long-range correlations and thus significantly reduces the sign problem of the quantum Monte Carlo cluster solver in the DCA +algorithm compared to the normal DCA. Simulations with much larger cluster sizes thus become feasible, which, along with the improved convergence in cluster size, raises hope that precise extrapolations to the exact infinite cluster size limit can be reached for other physical quantities as well.
UR - http://www.scopus.com/inward/record.url?scp=84884897088&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.88.115101
DO - 10.1103/PhysRevB.88.115101
M3 - Article
AN - SCOPUS:84884897088
SN - 1098-0121
VL - 88
JO - Physical Review B - Condensed Matter and Materials Physics
JF - Physical Review B - Condensed Matter and Materials Physics
IS - 11
M1 - 115101
ER -