A perturbative probabilistic approach to quantum many-body systems

作者：Di Stefano Andrea^*; Ostilli Massimo; Presilla Carlo

来源：Journal of Statistical Mechanics: Theory and Experiment , 2013, P04002.

DOI：10.1088/1742-5468/2013/04/P04002

• rigorous results in statistical mechanics
• quantum Monte Carlo simulations
• series expansions
• stochastic processes (theory)

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.

• 出版日期2013-4