Open AccessHigher Order Auxiliary Field Quantum Monte Carlo Methods
Author(s) -
Florian Goth
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2207/1/012029
Subject(s) - quantum monte carlo , auxiliary field , statistical physics , monte carlo method , hamiltonian (control theory) , physics , transformation (genetics) , field (mathematics) , quantum , mathematics , quantum mechanics , mathematical optimization , pure mathematics , biochemistry , statistics , chemistry , gene
The auxiliary field quantum Monte Carlo (AFQMC) method has been a workhorse in the field of strongly correlated electrons for a long time and has found its most recent implementation in the ALF package (alf.physik.uni-wuerzburg.de). The utilization of the Trotter decomposition to decouple the interaction from the non-interacting Hamiltonian makes this method inherently second order in terms of the imaginary time slice. We show that due to the use of the Hubbard-Stratonovich transformation (HST) a semigroup structure on the time evolution is imposed that necessitates the introduction of a new family of complex-hermitian splitting methods for the purpose of reaching higher order. We will give examples of these new methods and study their efficiency, as well as perform comparisons with other established second and higher order methods in the realm of the AFQMC method.