3 research outputs found
MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language
The Matsubara Green's function formalism stands as a powerful technique for
computing the thermodynamic characteristics of interacting quantum
many-particle systems at finite temperatures. In this manuscript, our focus
centers on introducing MatsubaraFunctions.jl, a Julia library that implements
data structures for generalized n-point Green's functions on Matsubara
frequency grids. The package's architecture prioritizes user-friendliness
without compromising the development of efficient solvers for quantum field
theories in equilibrium. Following a comprehensive introduction of the
fundamental types, we delve into a thorough examination of key facets of the
interface. This encompasses avenues for accessing Green's functions, techniques
for extrapolation and interpolation, as well as the incorporation of symmetries
and a variety of parallelization strategies. Examples of increasing complexity
serve to demonstrate the practical utility of the library, supplemented by
discussions on strategies for sidestepping impediments to optimal performance.Comment: 37 pages, 10 figure
Multiloop flow equations for single-boson exchange fRG
The recently introduced single-boson exchange (SBE) decomposition of the
four-point vertex of interacting fermionic many-body systems is a conceptually
and computationally appealing parametrization of the vertex. It relies on the
notion of reducibility of vertex diagrams with respect to the bare interaction
, instead of a classification based on two-particle reducibility within the
widely-used parquet decomposition. Here, we re-derive the SBE decomposition in
a generalized framework (suitable for extensions to, e.g., inhomogeneous
systems or real-frequency treatments) following from the parquet equations. We
then derive multiloop functional renormalization group (mfRG) flow equations
for the ingredients of this SBE decomposition, both in the parquet
approximation, where the fully two-particle irreducible vertex is treated as an
input, and in the more restrictive SBE approximation, where this role is taken
by the fully -irreducible vertex. Moreover, we give mfRG flow equations for
the popular parametrization of the vertex in terms of asymptotic classes of the
two-particle reducible vertices. Since the parquet and SBE decompositions are
closely related, their mfRG flow equations are very similar in structure.Comment: exchanged Sec. 3 and 4 and reordered appendices, added new Sec. 3.4
and App. D, extended the discussion in Sec. 2.3, 3.1, and 3.3, corrected Eq.
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