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Title: Inhomogeneous spectral moment sum rules for the retarded Green function and self-energy of strongly correlated electrons or ultracold fermionic atoms in optical lattices

Abstract

Spectral moment sum rules are presented for the inhomogeneous many-body problem described by the fermionic Falicov-Kimball or Hubbard models. These local sum rules allow for arbitrary hoppings, site energies, and interactions. They can be employed to quantify the accuracy of numerical solutions to the inhomogeneous many-body problem such as strongly correlated multilayered devices, ultracold atoms in an optical lattice with a trap potential, strongly correlated systems that are disordered, or systems with nontrivial spatial ordering such as a charge-density wave or a spin-density wave. We also show how the spectral moment sum rules determine the asymptotic behavior of the Green function, self-energy, and dynamical mean field when applied to the dynamical mean-field theory solution of the many-body problem. In particular, we illustrate in detail how one can dramatically reduce the number of Matsubara frequencies needed to solve the Falicov-Kimball model while still retaining high precision, and we sketch how one can incorporate these results into Hirsch-Fye quantum Monte Carlo solvers for the Hubbard (or more complicated) models. Since the solution of inhomogeneous problems is significantly more time consuming than periodic systems, efficient use of these sum rules can provide a dramatic speed up in the computational time required to solvemore » the many-body problem. We also discuss how these sum rules behave in nonequilibrium situations as well, where the Hamiltonian has explicit time dependence due to a driving field or due to the time-dependent change in a parameter such as the interaction strength or the origin of the trap potential.« less

Authors:
;  [1]
  1. Department of Physics, Georgetown University, Washington, DC 20057 (United States)
Publication Date:
OSTI Identifier:
21294339
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 80; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevB.80.115119; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ASYMPTOTIC SOLUTIONS; ATOMS; CHARGE DENSITY; ELECTRON CORRELATION; FERMIONS; GREEN FUNCTION; HAMILTONIANS; HUBBARD MODEL; INTERACTIONS; LASER RADIATION; MANY-BODY PROBLEM; MEAN-FIELD THEORY; MONTE CARLO METHOD; NUMERICAL SOLUTION; SPIN; SUM RULES; TIME DEPENDENCE

Citation Formats

Freericks, J K, Turkowski, V, and Department of Physics and Nanoscience and Technology Center, University of Central Florida, Orlando, Florida 32816. Inhomogeneous spectral moment sum rules for the retarded Green function and self-energy of strongly correlated electrons or ultracold fermionic atoms in optical lattices. United States: N. p., 2009. Web. doi:10.1103/PHYSREVB.80.115119.
Freericks, J K, Turkowski, V, & Department of Physics and Nanoscience and Technology Center, University of Central Florida, Orlando, Florida 32816. Inhomogeneous spectral moment sum rules for the retarded Green function and self-energy of strongly correlated electrons or ultracold fermionic atoms in optical lattices. United States. https://doi.org/10.1103/PHYSREVB.80.115119
Freericks, J K, Turkowski, V, and Department of Physics and Nanoscience and Technology Center, University of Central Florida, Orlando, Florida 32816. Tue . "Inhomogeneous spectral moment sum rules for the retarded Green function and self-energy of strongly correlated electrons or ultracold fermionic atoms in optical lattices". United States. https://doi.org/10.1103/PHYSREVB.80.115119.
@article{osti_21294339,
title = {Inhomogeneous spectral moment sum rules for the retarded Green function and self-energy of strongly correlated electrons or ultracold fermionic atoms in optical lattices},
author = {Freericks, J K and Turkowski, V and Department of Physics and Nanoscience and Technology Center, University of Central Florida, Orlando, Florida 32816},
abstractNote = {Spectral moment sum rules are presented for the inhomogeneous many-body problem described by the fermionic Falicov-Kimball or Hubbard models. These local sum rules allow for arbitrary hoppings, site energies, and interactions. They can be employed to quantify the accuracy of numerical solutions to the inhomogeneous many-body problem such as strongly correlated multilayered devices, ultracold atoms in an optical lattice with a trap potential, strongly correlated systems that are disordered, or systems with nontrivial spatial ordering such as a charge-density wave or a spin-density wave. We also show how the spectral moment sum rules determine the asymptotic behavior of the Green function, self-energy, and dynamical mean field when applied to the dynamical mean-field theory solution of the many-body problem. In particular, we illustrate in detail how one can dramatically reduce the number of Matsubara frequencies needed to solve the Falicov-Kimball model while still retaining high precision, and we sketch how one can incorporate these results into Hirsch-Fye quantum Monte Carlo solvers for the Hubbard (or more complicated) models. Since the solution of inhomogeneous problems is significantly more time consuming than periodic systems, efficient use of these sum rules can provide a dramatic speed up in the computational time required to solve the many-body problem. We also discuss how these sum rules behave in nonequilibrium situations as well, where the Hamiltonian has explicit time dependence due to a driving field or due to the time-dependent change in a parameter such as the interaction strength or the origin of the trap potential.},
doi = {10.1103/PHYSREVB.80.115119},
url = {https://www.osti.gov/biblio/21294339}, journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 11,
volume = 80,
place = {United States},
year = {2009},
month = {9}
}