Automatic computing of the grand potential in finite temperature many-body perturbation theory

Abstract

A new program created in C/C[Formula: see text] language generates automatically the analytic expression of grand potential and prints it in Latex2e format and in textual data. Another code created in Mathematica language can translate the textual data into a mathematical expression and help any interested to evaluate the thermodynamic quantities in analytic or numeric forms.

Finite and High-temperature series expansion via many-body perturbation theory

“…In previous work Ref. [12], we developed an algorithm to evaluate the Matsubara sums based on some basic definitions in graph theory. This method allows us to formulate the contribution Ω Gi n of each graph G i in terms of statistical factors f − , f + = 1 + f − and energies.…”

“…The arbitrary integer values of the edge coefficients n i > 0 can be determined by finding all the cycles of the directed graph G. For more details on the graphical evaluation of Matsubara sums and its algorithms, see our previous work Ref. [12].…”

“…In this case, our previous fast algorithm [11] could be used to generate all EDDs. The conventional DiagMC relies on the Matsubara formalism, but recently, a new algorithm was proposed to simplify the evaluation of diagrams [12][13][14]. In particular, this development revolves around reducing the integration of diagrams in space-time to only space.…”

“…In particular, this development revolves around reducing the integration of diagrams in space-time to only space. Our method [12] uses some basic definitions in graph theory, whereas the work of [13,14] is a direct application of residue theorem to each diagram. These methods reduce the calculation time and allow us to evaluate the grand potential or self-energy in the finite temperature of each order in MBPT.…”

Finite and high-temperature series expansion via many-body perturbation theory: application to Heisenberg spin-1/2 XXZ chain

“…In this case, our previous fast algorithm [11] could be used to generate this group of diagrams. The conventional DiagMC relies on the Matsubara formalism, but recently, a new algorithm was proposed to simplify the evaluation of diagrams [12][13][14]. In particular, this development revolves around reducing the integration of diagrams in space-time to only space.…”