2009/07/26 by J. K. Freericks, V. Turkowski, Volodymyr Turkowski · 1 citation
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Hamiltonian (control theory) #Hubbard model #Lattice (music) #Mathematics #Moment (physics) #Monte Carlo method #Optical lattice #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum Monte Carlo #Quantum and electron transport phenomena #Quantum chromodynamics #Quantum mechanics #Statistical physics #Sum rule in quantum mechanics #Wave function #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.80.115119
published as Phys. Rev. B 80, 115119 (2009) · (28 pages, 6 figures, ReVTeX) Paper updated to correct equations 11, 24, and 28
arxiv created 2009/07/26 · openalex publication_date 2009/09/22 · arxiv updated 2011/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.