QInchworm.topology_eval

Evaluator for strong-coupling expansion diagrams of a specific topology.

primitive type NodeKind <: Enum{Int32} 32

Node kind classification using @enum.

Possible values: pair_flag, identity_flag, inch_flag, operator_flag.

struct Node

Node in the atomic propagator backbone of a strong-coupling diagram.

Fields

• kind::QInchworm.topology_eval.NodeKind: Kind of the node

• arc_index::Int64: Index for pair interaction arc

• operator_index::Int64: Index of operator

struct FixedNode

Node in the atomic propagator backbone of a strong-coupling diagram fixed at a certain contour time point.

Fields

• node::QInchworm.topology_eval.Node: Reference to operator

• time::Keldysh.BranchPoint: Contour time point

PairNode(
    time::Keldysh.BranchPoint
) -> QInchworm.topology_eval.FixedNode

Return a node that serves as an end of a pair interaction arc fixed at time time.

IdentityNode(
    time::Keldysh.BranchPoint
) -> QInchworm.topology_eval.FixedNode

Return a fixed node at time time with an associated identity operator.

InchNode(
    time::Keldysh.BranchPoint
) -> QInchworm.topology_eval.FixedNode

Return a fixed 'inch' node at time time with an associated identity operator.

OperatorNode(
    time::Keldysh.BranchPoint,
    operator_pair_index::Int64,
    operator_index::Int64
) -> QInchworm.topology_eval.FixedNode

Return a fixed operator node at time time with an associated operator. The actual operator is stored in an Expansion structure and is uniquely identified by the pair (operator_pair_index, operator_index).

A type similar to SectorBlockMatrix, but storing two matrices per non-vanishing block. The two matrices represent an operator evaluated at the initial time and at a certain finite time.

EvolvingSectorBlockMatrix(
    sbm::Dict{Int64, Tuple{Int64, Matrix{ComplexF64}}}
) -> Dict{Int64, Tuple{Int64, Matrix{ComplexF64}, Matrix{ComplexF64}}}

Construct an EvolvingSectorBlockMatrix by setting both (initial and finite-time) matrices to those taken from a given SectorBlockMatrix.

get_finite_time(
    esbm::Dict{Int64, Tuple{Int64, Matrix{ComplexF64}, Matrix{ComplexF64}}},
    s::Int64
) -> Matrix{ComplexF64}

Get the finite-time matrix in esbm corresponding to the subspace s.

update_finite_time!(
    esbm::Dict{Int64, Tuple{Int64, Matrix{ComplexF64}, Matrix{ComplexF64}}},
    p
)

Update the finite-time matrices in esbm by multiplying the initial matrices by a block-diagonal matrix p.

struct TopologyEvaluator

The evaluation engine for the strong-coupling expansion diagrams.

In the following, a sequence of Node's contributing to a diagram of a certain topology is referred to as 'configuration'.

Fields

• exp::QInchworm.expansion.Expansion: Pseudo-particle expansion problem

• conf::Vector{QInchworm.topology_eval.Node}: Configuration as a list of nodes arranged in the contour order

• times::Vector{Keldysh.BranchPoint}: Contour positions of nodes in the configuration

• top_to_conf_pos::Vector{Int64}: Correspondence of node positions within a topology and a configuration

• var_time_pos::Vector{Int64}: Positions of variable time (non-fixed) nodes within a configuration

• use_bold_prop::Bool: Must the bold PPGFs be used?

• ppgf_mats::Matrix{Matrix{ComplexF64}}: PPGFs evaluated at all relevant pairs of time arguments. ppgf_mats[i, s] is the s-th diagonal block of exp.P (or exp.P0) evaluated at the pair of time points $(t_{i+1}, t_i)$.

• pair_ints::Matrix{ComplexF64}: Pair interaction arcs evaluated at all relevant pairs of time arguments.

  pair_ints[a, p] is the propagator from exp.pairs[p] evaluated at the pair of time points corresponding to the a-th arc in a topology.

• selected_pair_ints::Vector{Int64}: Indices of pair interactions within exp.pairs assigned to each interaction arc in a topology.

• top_result_mats::Vector{Matrix{ComplexF64}}: Pre-allocated container for per-topology evaluation results

• matrix_prods::Vector{QInchworm.utility.LazyMatrixProduct{ComplexF64}}: Pre-allocated matrix product evaluators, one per initial subspace

• node_mats::Vector{Union{Dict{Int64, Tuple{Int64, Matrix{ComplexF64}, Matrix{ComplexF64}}}, Matrix{Dict{Int64, Tuple{Int64, Matrix{ComplexF64}, Matrix{ComplexF64}}}}}}: Pre-allocated space for matrices of nodes multiplied by a PPGF from the right. For the pair nodes, matrices for all pair interactions are stored.

• result::Dict{Int64, Tuple{Int64, Matrix{ComplexF64}}}: Pre-allocated container for final evaluation result

• tmr::TimerOutputs.TimerOutput: Internal performance timer

TopologyEvaluator(
    exp::QInchworm.expansion.Expansion,
    order::Int64,
    use_bold_prop::Bool,
    fixed_nodes::Dict{Int64, QInchworm.topology_eval.FixedNode};
    tmr
) -> QInchworm.topology_eval.TopologyEvaluator

Parameters

• exp: Strong-coupling expansion problem.
• order: Expansion order of the diagrams (the number of interaction arcs).
• use_bold_prop: Must the bold PPGFs be used in the diagrams?
• fixed_nodes: List of fixed nodes in a configuration along with their positions.
• tmr: Internal performance timer.

Given a single diagram topology, evaluate contribution from all relevant configurations assuming that non-fixed nodes are located at contour time points times.

Given a list of diagram topologies, evaluate contribution from all relevant configurations assuming that non-fixed nodes are located at contour time points times.

_traverse_configuration_tree!(
    eval::QInchworm.topology_eval.TopologyEvaluator,
    pos::Int64,
    s_i::Int64,
    s_f::Int64,
    pair_int_weight::ComplexF64
) -> Union{Nothing, Bool, Int64}

Recursively traverse a tree of all configurations stemming from a given topology and contributing to the quantity of interest. The result is accumulated in eval.top_result_mats.

Parameters

• eval: Evaluator object.
• pos: Position of the currently processed Node in the configuration.
• s_i: Left block index of the matrix representation of the current node.
• s_f: Right block index expected at the final node.
• pair_int_weight: Current weight of the pair interaction contribution.