Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Computer Physics Communications

Computer-aided cluster expansion: An efficient algebraic approach for open quantum many-particle systems

A. Foerster, H. A. M. Leymann, Jan Wiersig

Published Oct 29, 2016• 7 citations
Publisher
DOI
10.1016/j.cpc.2016.10.010

Related papers

Cluster expansion of operator averages for systems of many particles

João da Providência

Nuclear Physics•Jul 1, 1963•23 citations

AB-INITIO COUPLED CLUSTER THEORY FOR OPEN QUANTUM SYSTEMS

G. Hagen, David J. Dean, T. Papenbrock +1 more

International Spring Seminar on Nuclear Physics•May 1, 2008•0 citations

Linked-cluster expansion around the atomic limit of the Hubbard model

Walter Metzner

We develop a perturbation expansion in the intersite hopping around the atomic limit of the Hubbard model. It is valid for arbitrary finite temperatures and interaction strengths. Diagrammatic rules that determine the grand-canonical potential and the Green's functions are derived. They reduce the calculation of any finite-order contribution to simple algebra. This opens the way for series extrapolations from computer-aided high-finite-order evaluations. Discrepancies in earlier expansions around the atomic limit are clarified. The present expansion scheme involves only connected diagrams with unrestricted lattice sums. This allows one to perform a vertex renormalization as for the linked-cluster expansion of the Ising model. The renormalized perturbation expansion can be used to construct self-consistent approximations which are automatically exact in the atomic limit. In the limit of high lattice dimensions, only fully two-particle reducible embeddings of diagrams on the lattice contribute. The single-particle properties of the infinite-dimensional Hubbard model reduce to those of independent tight-binding fermions hopping between dressed sites.

Physical review. B, Condensed matter•Apr 1, 1991•239 citations

Expectation value based cluster expansion

H. A. M. Leymann, A. Foerster, Jan Wiersig

Abstract We outline a new formulation of the cluster expansion to derive equations of motion for open quantum systems. Our method uses expectation values instead of correlation functions. The algebraic effort to derive the equations is reduced and the approach is more intuitive. We demonstrate the efficiency of our method by applying it to the damped Jaynes‐Cummings model. This model is a good starting point to investigate quantum dot based laser systems. Further we will examine the convergence properties of the cluster expansion for various orders. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics•Jun 7, 2013•12 citations

Coupled-cluster methods for open-shell molecular and other many-fermion systems

Gour, Jeffrey R.

•Jan 1, 2010•0 citations

The cluster expansion for classical and quantum lattice systems

Yong‐Moon Park

Journal of Statistical Physics•Mar 1, 1982•26 citations
We develop a perturbation expansion in the intersite hopping around the atomic limit of the Hubbard model. It is valid for arbitrary finite temperatures and interaction strengths. Diagrammatic rules that determine the grand-canonical potential and the Green's functions are derived. They reduce the calculation of any finite-order contribution to simple algebra. This opens the way for series extrapolations from computer-aided high-finite-order evaluations. Discrepancies in earlier expansions around the atomic limit are clarified. The present expansion scheme involves only connected diagrams with unrestricted lattice sums. This allows one to perform a vertex renormalization as for the linked-cluster expansion of the Ising model. The renormalized perturbation expansion can be used to construct self-consistent approximations which are automatically exact in the atomic limit. In the limit of high lattice dimensions, only fully two-particle reducible embeddings of diagrams on the lattice contribute. The single-particle properties of the infinite-dimensional Hubbard model reduce to those of independent tight-binding fermions hopping between dressed sites.
Abstract We outline a new formulation of the cluster expansion to derive equations of motion for open quantum systems. Our method uses expectation values instead of correlation functions. The algebraic effort to derive the equations is reduced and the approach is more intuitive. We demonstrate the efficiency of our method by applying it to the damped Jaynes‐Cummings model. This model is a good starting point to investigate quantum dot based laser systems. Further we will examine the convergence properties of the cluster expansion for various orders. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)