Operators

Operators in Schwinger.jl are represented by the abstract type SchwingerOperator, with three concrete types:

EDOperator: an operator represented as a matrix for its action on a basis of BasisStates
ITensorOperator: a matrix product operator using ITensorMPS.jl
MPSKitOperator: a matrix product operator using MPSKit.jl

Unified API

Like the Hamiltonian, other operators can be constructed using the unified API with the backend keyword:

W = WilsonLoop(lattice; backend=:ED)
W = WilsonLoop(lattice; backend=:ITensors)
W = WilsonLoop(lattice; backend=:MPSKit)

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

using Schwinger
lat = Lattice(10; F = 1, )
gs = groundstate(Hamiltonian(lat; backend=:ED))

sum(electricfields(gs))/10, expectation(AverageElectricField(lat; backend=:ED), gs)

(-0.06311875619670917, -0.06311875619670704 + 1.7347234759768063e-18im)

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

using LinearAlgebra
dot(gs, AverageElectricField(lat; backend=:ED) * gs)

-0.06311875619670707 + 1.734723475976807e-18im

Schwinger.expectation — Function

expectation(op, state)

Return the expectation value of the operator op in state.

Arguments

op::EDOperator`: operator.
state::EDState: state.

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expectation(op, state)

Return the expectation value of the operator op in state.

Arguments

op::ITensorOperator`: operator.
state::ITensorState: state.

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expectation(op, state)

Return the expectation value of the operator op in state.

Arguments

op::MPSKitOperator`: operator.
state::MPSKitState: state.

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Schwinger.act — Function

act(op, state)

Apply the operator op to the state state.

Arguments

op::ITensorOperator: operator.
state::ITensorState: state.

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act(op, state)

Apply the operator op to the state state.

Arguments

op::EDOperator: operator.
state::EDState: state.

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act(op, state)

Apply the operator op to the state state.

Arguments

op::MPSKitOperator: operator.
state::MPSKitState: state.

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Exact diagonalization

Schwinger.EDWilsonLoop — Function

wilsonloop(hamiltonian, conjugate = false)

Returns the spatial Wilson loop operator for lattice.

Arguments

lattice::Lattice: 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::Lattice: 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::Lattice: 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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ITensors operators

Schwinger.ITensorWilsonLoop — Function

ITensorWilsonLoop(lattice, conjugate = false)

Returns the spatial Wilson loop operator for lattice.

Arguments

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

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Schwinger.ITensorWilsonLine — Function

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

Returns the spatial Wilson line operator for lattice.

Arguments

lattice::Lattice: 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.ITensorAverageElectricField — Function

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

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

Arguments

lattice::Lattice: 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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MPSKit operators

Schwinger.MPSKitWilsonLoop — Function

MPSKitWilsonLoop(lattice, conjugate = false)

Returns the spatial Wilson loop operator for lattice using MPSKit.

Arguments

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

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Schwinger.MPSKitWilsonLine — Function

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

Returns the spatial Wilson line operator for lattice using MPSKit.

Arguments

lattice::Lattice: 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.MPSKitAverageElectricField — Function

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

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

Arguments

lattice::Lattice: The lattice to compute the average electric field on.
power::Int=1: The power to raise the electric field to.
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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