Operators

Operators in Schwinger.jl are represented by the abstract type SchwingerOperator, with two descendants:

EDOperator: an operator represented as a matrix for its action on a basis of SchwingerBasisStates
MPOOperator: a matrix product operator, stored as an MPO object using ITensorMPS.jl

We can evaluate the expectation of an operator in a state:

using Schwinger
lat = SchwingerLattice{10,1}()
gs = groundstate(EDHamiltonian(lat))

sum(electricfields(gs))/10, expectation(EDAverageElectricField(lat), gs)

(-0.06311875619670844, -0.06311875619670718 + 2.1684043449710118e-19im)

This can also be carried out manually by acting on the state with the operator:

using LinearAlgebra
dot(gs, EDAverageElectricField(lat) * gs)

-0.0631187561967071 + 2.168404344971009e-19im

Schwinger.expectation — Function

expectation(op, state)

Return the expectation value of the operator op in state.

Arguments

op::EDOperator{N,F}`: operator.
state::SchwingerEDState: state.

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expectation(op, state)

Return the expectation value of the operator op in state.

Arguments

op::MPOOperator{N,F}`: operator.
state::SchwingerMPS: state.

source

Schwinger.act — Function

act(op, state)

Apply the operator op to the state state.

Arguments

op::MPOOperator{N,F}: operator.
state::SchwingerMPS{N,F}: state.

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act(op, state)

Apply the operator op to the state state.

Arguments

op::EDOperator{N,F}: operator.
state::SchwingerEDState{N,F}: state.

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Exact diagonalization

Schwinger.EDWilsonLoop — Function

wilsonloop(hamiltonian, conjugate = false)

Returns the spatial Wilson loop operator for lattice.

Arguments

lattice::SchwingerLattice: lattice.
conjugate::Bool: Conjugation of the Wilson loop.

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Schwinger.EDWilsonLine — Function

EDWilsonLine(lattice, conjugate = false, flavor = 1, start = 1, finish = N)

Returns the spatial Wilson line operator for lattice.

Arguments

lattice::SchwingerLattice: lattice.
conjugate::Bool: Conjugation of the Wilson line.
flavor::Int: Flavor of the Wilson line.
start::Int: Starting site of the Wilson line.
finish::Int: Finishing site of the Wilson line.

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Schwinger.EDAverageElectricField — Function

EDAverageElectricField(lattice; power = 1, L_max = nothing, universe = 0)

Construct an EDOperator that computes the average electric field (raised to some power).

Arguments

lattice::SchwingerLattice{N,F}: The lattice to compute the average electric field on.
power::Int=1: The power to raise the electric field to.
L_max::Union{Nothing,Int}=nothing: The maximum absolute value of L₀.
universe::Int=0: The universe to compute the average electric field in.
sitelist::Union{Nothing,Vector{Int}}=nothing: List of sites to average over.

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Matrix product operators

Schwinger.MPOWilsonLoop — Function

wilsonloop(hamiltonian, conjugate = false)

Returns the spatial Wilson loop operator for lattice.

Arguments

lattice::SchwingerLattice: lattice.
conjugate::Bool: Conjugation of the Wilson loop.

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Schwinger.MPOWilsonLine — Function

MPOWilsonLine(lattice, conjugate = false, flavor = 1, start = 1, finish = N)

Returns the spatial Wilson line operator for lattice.

Arguments

lattice::SchwingerLattice: lattice.
conjugate::Bool: Conjugation of the Wilson line.
flavor::Int: Flavor of the Wilson line.
start::Int: Starting site of the Wilson line.
finish::Int: Finishing site of the Wilson line.

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Schwinger.MPOAverageElectricField — Function

MPOAverageElectricField(lattice; power = 1, L_max = nothing, universe = 0)

Construct an MPOOperator that computes the average electric field (raised to some power).

Arguments

lattice::SchwingerLattice{N,F}: The lattice to compute the average electric field on.
power::Int=1: The power to raise the electric field to.
L_max::Union{Nothing,Int}=nothing: The maximum absolute value of L₀.
universe::Int=0: The universe to compute the average electric field in.
sitelist::Union{Nothing,Vector{Int}}=nothing: List of sites to average over.

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