2012/10/31 by Andrea Di Stefano, Massimo Ostilli, Carlo Presilla · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Boson #Cold Atom Physics and Bose-Einstein Condensates #Cumulant #Nonlinear system #Probabilistic logic #Probability distribution #Quantum #Quantum many-body systems #Scalar (mathematics) #Uncorrelated #cond-mat.stat-mech #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/1742-5468/2013/04/p04002
published in Journal of Statistical Mechanics Theory and Experiment 2013(04), P04002 (Institute of Physics) · 39 pages, 1 picture, 5 figures
arxiv created 2013/04/02 · openalex publication_date 2013/04/02 · arxiv updated 2013/04/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In the probabilistic approach to quantum many-body systems, the ground-state energy is the solution of a nonlinear scalar equation written either as a cumulant expansion or as an expectation with respect to a probability distribution of the potential and hopping (amplitude and phase) values recorded during an infinitely lengthy evolution. We introduce a perturbative expansion of this probability distribution which conserves, at any order, a multinomial-like structure, typical of uncorrelated systems, but includes, order by order, the statistical correlations provided by the cumulant expansion. The proposed perturbative scheme is successfully tested in the case of pseudo-spin 1/2 hardcore boson Hubbard models also when affected by a phase problem due to an applied magnetic field.